{"segment":[{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["6"]]],"list":[{"point":5,"width":40,"content":"","type_input":"","type_check":"","ques":"Gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh:$\\dfrac{9x-7}{\\sqrt{7x+5}}=\\sqrt{7x+5}$ <br\/> T\u1eadp nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh l\u00e0: $S=\\{\\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{}\\}$ ","hint":"\u00c1p d\u1ee5ng: $\\dfrac{a}{b}=\\dfrac{c}{d}\\Leftrightarrow ad=bc$","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/><b>B\u01b0\u1edbc 1:<\/b> T\u00ecm \u0111i\u1ec1u ki\u1ec7n x\u00e1c \u0111\u1ecbnh c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh.<br\/><b>B\u01b0\u1edbc 2:<\/b> Gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh <br\/><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/>\u0110i\u1ec1u ki\u1ec7n $7x+5>0\\Leftrightarrow x>-\\dfrac{5}{7}$ <br\/>$\\begin{aligned} & \\dfrac{9x-7}{\\sqrt{7x+5}}\\,\\,\\,\\,\\,=\\sqrt{7x+5} \\\\ & \\Leftrightarrow 9x-7\\,\\,=7x+5 \\\\ & \\Leftrightarrow 2x\\,\\,\\,\\,\\,\\,\\,\\,\\,=12 \\\\ & \\Leftrightarrow x\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,=6 \\\\ \\end{aligned}$<br\/>T\u1eadp nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh l\u00e0 $S=\\{6\\}$<br\/><span class='basic_pink'>V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n l\u00e0 $6$<\/span><\/span><\/span>"}]}],"id_ques":531},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank_random","correct":[[["4","-4"],["-4","4"]]],"list":[{"point":5,"width":40,"content":"","type_input":"","type_check":"","ques":"Gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh: $\\sqrt{4\\left( {{x}^{2}}-1 \\right)}-2\\sqrt{15}=0$<br\/> \u0110\u00e1p s\u1ed1: $\\left[ \\begin{array}{} x= \\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{} \\\\ x = \\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{} \\end{array} \\right.$ ","hint":"Bi\u1ebfn \u0111\u1ed5i ph\u01b0\u01a1ng tr\u00ecnh v\u1ec1 d\u1ea1ng $\\sqrt{A} =b$","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/><b>B\u01b0\u1edbc 1:<\/b> T\u00ecm \u0111i\u1ec1u ki\u1ec7n x\u00e1c \u0111\u1ecbnh c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh.<br\/><b>B\u01b0\u1edbc 2:<\/b>Bi\u1ebfn \u0111\u1ed5i ph\u01b0\u01a1ng tr\u00ecnh v\u1ec1 d\u1ea1ng $\\sqrt A=b$<br\/><b>B\u01b0\u1edbc 3:<\/b> B\u00ecnh ph\u01b0\u01a1ng hai v\u1ebf v\u00e0 gi\u1ea3i ti\u1ebfp ph\u01b0\u01a1ng tr\u00ecnh. <br\/><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> \u0110i\u1ec1u ki\u1ec7n: ${{x}^{2}}-1\\ge 0\\Leftrightarrow \\left| x \\right|>1$ <br\/>$\\begin{align} & \\sqrt{4\\left( {{x}^{2}}-1 \\right)}-2\\sqrt{15}=0 \\\\ & \\Leftrightarrow 2\\sqrt{{{x}^{2}}-1}\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,=2\\sqrt{15} \\\\ & \\Leftrightarrow {{\\left( \\sqrt{{{x}^{2}}-1} \\right)}^{2}}\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,={{\\left( \\sqrt{15} \\right)}^{2}} \\\\ & \\Leftrightarrow {{x}^{2}}-1\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,=15 \\\\ & \\Leftrightarrow {{x}^{2}}\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,=16 \\\\ & \\Leftrightarrow x\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,=\\pm 4 \\\\ \\end{align}$ <br\/>(th\u1ecfa m\u00e3n \u0111i\u1ec1u ki\u1ec7n v\u00ec $\\left| \\pm 4 \\right|=4>1$ )<br\/>V\u1eady t\u1eadp nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh l\u00e0 $S=\\{4; -4\\}$ <br\/><span class='basic_pink'>V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n l\u00e0 $4$ v\u00e0 $-4$<\/span><\/span><\/span>"}]}],"id_ques":532},{"time":24,"part":[{"title":"\u0110i\u1ec1n d\u1ea5u $> , < , =$ v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[[">"]]],"list":[{"point":5,"width":40,"content":"","type_input":"","type_check":"","ques":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/daiso/bai3/lv2/img\/5.jpg' \/><\/center><br\/>$\\sqrt{27}+\\sqrt{6}+1$ _input_ $\\sqrt{48}$ ","hint":"X\u00e9t hi\u1ec7u: $(\\sqrt{27}+\\sqrt{6}+1)-\\sqrt{48}$","explain":"<span class='basic_left'>Ta c\u00f3:<br\/>$\\begin{align} & \\sqrt{27}+\\sqrt{6}+1-\\sqrt{48} \\\\ & =\\sqrt{3}.\\sqrt{9}+\\sqrt{6}+1-\\sqrt{3}.\\sqrt{16} \\\\ & =3\\sqrt{3}+\\sqrt{6}+1-4\\sqrt{3} \\\\ & =\\sqrt{6}-\\sqrt{3}+1\\,\\,\\, \\\\ \\end{align}$ <br\/> V\u00ec $\\sqrt 6 >\\sqrt 3$ n\u00ean $\\sqrt{6}-\\sqrt{3}+1>0$<br\/>Suy ra, $\\sqrt{27}+\\sqrt{6}+1 > \\sqrt{48}$ <br\/><span class='basic_pink'>V\u1eady d\u1ea5u c\u1ea7n \u0111i\u1ec1n l\u00e0 $>$<\/span><\/span>"}]}],"id_ques":533},{"time":24,"part":[{"title":"\u0110i\u1ec1n d\u1ea5u $> , < , =$ v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[[">"]]],"list":[{"point":5,"width":40,"content":"","type_input":"","type_check":"","ques":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/daiso/bai3/lv2/img\/5.jpg' \/><\/center><br\/> $\\sqrt{5}+\\sqrt{7}$ _input_ $\\sqrt{12}$ ","hint":"So s\u00e1nh gi\u00e1 tr\u1ecb b\u00ecnh ph\u01b0\u01a1ng c\u1ee7a hai v\u1ebf. \u00c1p d\u1ee5ng: V\u1edbi $a, b$ d\u01b0\u01a1ng, $a^2>b^2$ th\u00ec $a>b.$","explain":"<span class='basic_left'>Ta c\u00f3:<br\/>${{\\left( \\sqrt{5}+\\sqrt{7} \\right)}^{2}}=5+2.\\sqrt{5}.\\sqrt{7}+7\\,\\,$$=12+2\\sqrt{35}>{{\\left( \\sqrt{12} \\right)}^{2}}$<br\/>Do \u0111\u00f3 $\\sqrt{5}+\\sqrt{7} >\\sqrt{12}$ <br\/><span class='basic_pink'>V\u1eady d\u1ea5u c\u1ea7n \u0111i\u1ec1n l\u00e0 $>$ <\/span> <\/span>"}]}],"id_ques":534},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["-1"],["2"]]],"list":[{"point":5,"width":40,"content":"","type_input":"","type_check":"","ques":"T\u00ednh gi\u00e1 tr\u1ecb bi\u1ec3u th\u1ee9c: $D=\\dfrac{x-\\sqrt{5}}{x\\left( x-\\sqrt{5} \\right)+\\sqrt{2}\\left( x-\\sqrt{5} \\right)}$ t\u1ea1i $x=-2\\sqrt{2}$ <br\/>\u0110\u00e1p s\u1ed1: $D=\\dfrac{\\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{}}{\\sqrt{\\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{}}}$ ","hint":"Ph\u00e2n t\u00edch m\u1eabu th\u1ee9c th\u00e0nh nh\u00e2n t\u1eed ","explain":"<span class='basic_left'>\u0110i\u1ec1u ki\u1ec7n: $x\\ne \\sqrt{5}$<br\/>Ta c\u00f3:<br\/>$\\begin{align}D&=\\dfrac{x-\\sqrt{5}}{x\\left( x-\\sqrt{5} \\right)+\\sqrt{2}\\left( x-\\sqrt{5} \\right)}\\\\&=\\dfrac{x-\\sqrt{5}}{\\left( x-\\sqrt{5} \\right)\\left( x+\\sqrt{2} \\right)}\\\\&=\\dfrac{1}{x+\\sqrt{2}}\\\\ \\end{align}$<br\/>Thay $x= -2\\sqrt{2}$ v\u00e0o bi\u1ec3u th\u1ee9c $D$ \u0111\u00e3 r\u00fat g\u1ecdn, ta \u0111\u01b0\u1ee3c: $D=\\dfrac{1}{-2\\sqrt{2}+\\sqrt{2}}=-\\dfrac{1}{\\sqrt{2}}$ <br\/><span class='basic_pink'>V\u1eady c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng \u0111\u1ec3 $D=-\\dfrac{1}{\\sqrt{2}}$ <\/span> <\/span>"}]}],"id_ques":535},{"time":24,"part":[{"title":"Ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang","title_trans":"","temp":"multiple_choice","correct":[[1]],"list":[{"point":5,"select":["A. $\\dfrac{1}{2}$","B. $\\dfrac{1}{4}$","C. $\\dfrac{3}{2}$"],"ques":"T\u00ednh gi\u00e1 tr\u1ecb bi\u1ec3u th\u1ee9c: $A=\\dfrac{x\\sqrt{x}+y\\sqrt{y}}{\\sqrt{x}+\\sqrt{y}}-{{\\left( \\sqrt{x}-\\sqrt{y} \\right)}^{2}}$ t\u1ea1i $x=\\dfrac{1}{2};\\,\\,y=\\dfrac{1}{2}$ <br\/>\u0110\u00e1p s\u1ed1: $A=$?","hint":"\u0110\u01b0a $x$ v\u00e0 $y$ v\u00e0o trong c\u0103n th\u1ee9c r\u1ed3i r\u00fat g\u1ecdn bi\u1ec3u th\u1ee9c v\u00e0 th\u1ef1c hi\u1ec7n t\u00ednh gi\u00e1 tr\u1ecb c\u1ee7a bi\u1ec3u th\u1ee9c.","explain":"<span class='basic_left'>\u0110i\u1ec1u ki\u1ec7n : $x,y\\ge 0$ v\u00e0 $x,y$ kh\u00f4ng \u0111\u1ed3ng th\u1eddi b\u1eb1ng $0$.<br\/>Ta c\u00f3: $A=\\dfrac{x\\sqrt{x}+y\\sqrt{y}}{\\sqrt{x}+\\sqrt{y}}-{{\\left( \\sqrt{x}-\\sqrt{y} \\right)}^{2}}$<br\/>$=\\dfrac{{\\sqrt{x}}^3+{\\sqrt{y}}^3}{\\sqrt{x}+\\sqrt{y}}-\\left( x-2\\sqrt{xy}+y \\right) $<br\/>$=\\dfrac{\\left( \\sqrt{x}+\\sqrt{y} \\right)\\left( x-\\sqrt{xy}+y \\right)}{\\sqrt{x}+\\sqrt{y}}\\,$$-x+2\\sqrt{xy}-y $<br\/>$ =x-\\sqrt{xy}+y-x+2\\sqrt{xy}-y$<br\/>$=\\sqrt{xy} $<br\/>Thay $x=\\dfrac{1}{2};\\,\\,y=\\dfrac{1}{2}$ v\u00e0o bi\u1ec3u th\u1ee9c $A$ \u0111\u00e3 r\u00fat g\u1ecdn, ta \u0111\u01b0\u1ee3c: $A=\\sqrt{\\dfrac{1}{2}.\\dfrac{1}{2}}=\\dfrac{1}{2}$<\/span>"}]}],"id_ques":536},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["-2"]]],"list":[{"point":5,"width":40,"content":"","type_input":"","type_check":"","ques":"R\u00fat g\u1ecdn: $\\sqrt{{{\\left( 1-\\sqrt{3} \\right)}^{2}}}-\\sqrt{4+2\\sqrt{3}}=$_input_","hint":"Bi\u1ebfn \u0111\u1ed5i bi\u1ec3u th\u1ee9c trong c\u0103n v\u1ec1 h\u1eb1ng \u0111\u1eb3ng th\u1ee9c $(A \\pm B)^2$. ","explain":"<span class='basic_left'>Ta c\u00f3:<br\/>$\\begin{align} & \\sqrt{{{\\left( 1-\\sqrt{3} \\right)}^{2}}}-\\sqrt{4+2\\sqrt{3}} \\\\ & =\\left| 1-\\sqrt{3} \\right|-\\sqrt{(\\sqrt{3})^2+2.\\sqrt{3}.1+{{1}^{2}}} \\\\ & =\\sqrt{3}-1-\\sqrt{{{\\left( \\sqrt{3}+1 \\right)}^{2}}} \\,(V\u00ec\\,\\sqrt{3}>1)\\\\ & =\\sqrt{3}-1-\\sqrt{3}-1 \\\\ & =-2 \\\\\\end{align}$ <br\/><span class='basic_pink'>V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u00e0 $-2$<\/span><\/span><\/span><\/span>"}]}],"id_ques":537},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank_random","correct":[[["3"]]],"list":[{"point":5,"width":40,"content":"","type_input":"","type_check":"","ques":"T\u00ednh $\\dfrac{\\sqrt{405}+3\\sqrt{27}}{3\\sqrt{3}+\\sqrt{45}}=$_input_","hint":"Ph\u00e2n t\u00edch \u0111a th\u1ee9c th\u00e0nh nh\u00e2n t\u1eed ","explain":"<span class='basic_left'>Ta c\u00f3:<br\/>$\\begin{align} & \\dfrac{\\sqrt{405}+3\\sqrt{27}}{3\\sqrt{3}+\\sqrt{45}} \\\\ & =\\dfrac{\\sqrt{81}.\\sqrt{5}+3.\\sqrt{3}.\\sqrt{9}}{3\\sqrt{3}+\\sqrt{9}.\\sqrt{5}} \\\\ & =\\dfrac{9\\sqrt{5}+9\\sqrt{3}}{3\\sqrt{3}+3\\sqrt{5}} \\\\ & =\\dfrac{9\\left( \\sqrt{5}+\\sqrt{3} \\right)}{3\\left( \\sqrt{3}+\\sqrt{5} \\right)}=3 \\\\\\end{align}$<br\/><span class='basic_pink'>V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u00e0 $3$<\/span><\/span> <\/span>"}]}],"id_ques":538},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["1"]]],"list":[{"point":5,"width":40,"content":"","type_input":"","type_check":"","ques":"Th\u1ef1c hi\u1ec7n ph\u00e9p t\u00ednh: $\\sqrt{{{\\left( 3-\\sqrt{3} \\right)}^{2}}}.\\sqrt{\\dfrac{1}{12-6\\sqrt{3}}}=$_input_","hint":"","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/><b>B\u01b0\u1edbc 1:<\/b> Bi\u1ebfn \u0111\u1ed5i $\\sqrt{12-6\\sqrt{3}}$ v\u1ec1 d\u1ea1ng $\\sqrt{(3- \\sqrt{3})^2}$<br\/><b>B\u01b0\u1edbc 2:<\/b> Nh\u00e2n hai bi\u1ec3u th\u1ee9c d\u01b0\u1edbi d\u1ea5u c\u0103n sau \u0111\u00f3 bi\u1ebfn \u0111\u1ed5i v\u00e0 r\u00fat g\u1ecdn.<br\/><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/>Ta c\u00f3:<br\/>$\\begin{align}&\\,\\,\\,\\,\\sqrt{{{\\left( 3-\\sqrt{3} \\right)}^{2}}}.\\sqrt{\\dfrac{1}{12-6\\sqrt{3}}}\\\\&=\\sqrt{\\dfrac{{{\\left( 3-\\sqrt{3} \\right)}^{2}}}{{{3}^{2}}-2.3.\\sqrt{3}+(\\sqrt{3})^2}}\\\\&=\\sqrt{\\dfrac{{{\\left( 3-\\sqrt{3} \\right)}^{2}}}{{{\\left( 3-\\sqrt{3} \\right)}^{2}}}}\\\\&=1\\\\ \\end{align}$ <br\/><span class='basic_pink'>V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u00e0 $1$<\/span><br\/><span class='basic_green'>L\u01b0u \u00fd:<\/span><br\/>N\u1ebfu $a\\ge0, b\\ge0$ th\u00ec $\\sqrt{a}.\\sqrt{b}=\\sqrt{a.b}$<\/span><\/span> "}]}],"id_ques":539},{"time":24,"part":[{"title":"Ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang","title_trans":"","temp":"multiple_choice","correct":[[2]],"list":[{"point":5,"select":["A. $\\dfrac{1}{2}$","B. $\\dfrac{5}{2}$","C. $\\dfrac{3}{2}$"],"ques":"Th\u1ef1c hi\u1ec7n ph\u00e9p t\u00ednh: $\\sqrt{\\dfrac{1}{8}}.\\sqrt{2}.\\sqrt{125}.\\sqrt{\\dfrac{1}{5}}=$?","hint":"\u00c1p d\u1ee5ng: N\u1ebfu $a\\ge0, b\\ge0$ th\u00ec $\\sqrt{a}.\\sqrt{b}=\\sqrt{a.b}$ ","explain":"<span class='basic_left'>Ta c\u00f3:<br\/>$\\sqrt{\\dfrac{1}{8}}.\\sqrt{2}.\\sqrt{125}.\\sqrt{\\dfrac{1}{5}}\\,\\,$$=\\sqrt{\\dfrac{1}{8}.2.125.\\dfrac{1}{5}}\\,\\,$$=\\sqrt{\\dfrac{25}{4}}=\\dfrac{5}{2}$<\/span>"}]}],"id_ques":540},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["420"]]],"list":[{"point":5,"width":40,"content":"","type_input":"","type_check":"","ques":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/daiso/bai3/lv2/img\/4.jpg' \/><\/center> T\u00ednh gi\u00e1 tr\u1ecb bi\u1ec3u th\u1ee9c $\\sqrt{5}.\\sqrt{30}.\\sqrt{42}.\\sqrt{28}=$_input_","hint":"\u00c1p d\u1ee5ng: N\u1ebfu $a\\ge0, b\\ge0$ th\u00ec $\\sqrt{a}.\\sqrt{b}=\\sqrt{a.b}$ ","explain":"<span class='basic_left'>Ta c\u00f3:<br\/>$\\begin{align} & \\sqrt{5}.\\sqrt{30}.\\sqrt{42}.\\sqrt{28} \\\\ & =\\sqrt{5.30.42.28} \\\\ & =\\sqrt{5.5.6.6.7.7.4} \\\\ & =5.6.7.2\\\\ & =420 \\\\ \\end{align}$ <br\/><span class='basic_pink'>V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u00e0 $420$ <\/span> <\/span>"}]}],"id_ques":541},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["60"]]],"list":[{"point":5,"width":40,"content":"","type_input":"","type_check":"","ques":" <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/daiso/bai3/lv2/img\/2.jpg' \/><br\/>T\u00ednh gi\u00e1 tr\u1ecb bi\u1ec3u th\u1ee9c sau:$\\sqrt{{{68}^{2}}-{{32}^{2}}}=$_input_","hint":"\u00c1p d\u1ee5ng h\u1eb1ng \u0111\u1eb3ng th\u1ee9c $a^2-b^2$","explain":"<span class='basic_left'>Ta c\u00f3:<br\/>$\\begin{align}&\\,\\,\\,\\,\\sqrt{{{68}^{2}}-{{32}^{2}}}\\\\&=\\sqrt{\\left( 68-32 \\right)\\left( 68+32 \\right)}\\\\&=\\sqrt{36.100}\\\\ &=\\sqrt{36}.\\sqrt{100}\\\\ &=6.10\\\\ &=60\\\\ \\end{align}$<br\/><br\/><span class='basic_pink'>V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u00e0 $60$ <\/span><\/span> "}]}],"id_ques":542},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["0"]]],"list":[{"point":5,"width":40,"content":"","type_input":"","type_check":"","ques":" T\u00ednh gi\u00e1 tr\u1ecb bi\u1ec3u th\u1ee9c: $B=\\sqrt{252}-\\sqrt{700}+\\sqrt{1008}-\\sqrt{448}$<br\/>\u0110\u00e1p s\u1ed1 $B=$_input_","hint":"T\u00e1ch m\u1ed7i s\u1ed1 d\u01b0\u1edbi d\u1ea5u c\u0103n v\u1ec1 d\u1ea1ng $a^2.b$ r\u1ed3i \u00e1p d\u1ee5ng: $\\sqrt{a^2b}=a\\sqrt b$","explain":"<span class='basic_left'>Ta c\u00f3:<br\/>$B=\\sqrt{252}-\\sqrt{700}+\\sqrt{1008}-\\sqrt{448}$<br\/>$ =\\sqrt{36.7}-\\sqrt{7.100}+\\sqrt{7.144}-\\sqrt{64.7} $<br\/>$=\\sqrt{7}\\left( \\sqrt{36}-\\sqrt{100}+\\sqrt{144}-\\sqrt{64} \\right) $<br\/>$=\\sqrt{7}\\left( 6-10+12-8 \\right) $<br\/>$ =0 $ <br\/><span class='basic_pink'>V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u00e0 $0$ <\/span><\/span>"}]}],"id_ques":543},{"time":24,"part":[{"title":"Ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang","title_trans":"","temp":"multiple_choice","correct":[[3]],"list":[{"point":5,"select":["A. $\\sqrt{2}$","B. $5\\sqrt{2}$","C. $9\\sqrt{2}$"],"ques":"T\u00ednh gi\u00e1 tr\u1ecb bi\u1ec3u th\u1ee9c: $A=\\sqrt{50}-\\sqrt{18}+\\sqrt{162}-2\\sqrt{2}$<br\/>\u0110\u00e1p s\u1ed1: $A=$?","hint":"T\u00e1ch m\u1ed7i s\u1ed1 d\u01b0\u1edbi d\u1ea5u c\u0103n v\u1ec1 d\u1ea1ng $a^2.b$ r\u1ed3i \u00e1p d\u1ee5ng: $\\sqrt{a^2b}=a\\sqrt b$","explain":"<span class='basic_left'>Ta c\u00f3:<br\/>$ A=\\sqrt{50}-\\sqrt{18}+\\sqrt{162}-2\\sqrt{2} $<br\/>$ =\\sqrt{2.25}-\\sqrt{2.9}+\\sqrt{2.81}-2\\sqrt{2}$<br\/>$=\\sqrt{2}.\\sqrt{25}-\\sqrt{2}.\\sqrt{9}+\\sqrt{2}.\\sqrt{81}-2\\sqrt{2} $<br\/>$ =5\\sqrt{2}-3\\sqrt{2}+9\\sqrt{2}-2\\sqrt{2}$<br\/>$ =9\\sqrt{2}$<\/span>"}]}],"id_ques":544},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[1]],"list":[{"point":5,"ques":"K\u1ebft qu\u1ea3 c\u1ee7a ph\u00e9p t\u00ednh $\\sqrt{12}+2\\sqrt{27}+3\\sqrt{75}-9\\sqrt{48}$ l\u00e0: ","select":["A. $-13\\sqrt{3}$","B. $13\\sqrt{3}$ ","C. $\\sqrt{3}$","D. $-9\\sqrt{3}$ "],"hint":"T\u00e1ch m\u1ed7i s\u1ed1 d\u01b0\u1edbi d\u1ea5u c\u0103n v\u1ec1 d\u1ea1ng $a^2.b$ r\u1ed3i \u00e1p d\u1ee5ng: $\\sqrt{a^2b}=a\\sqrt b$","explain":"<span class='basic_left'>Ta c\u00f3:<br\/>$ \\sqrt{12}+2\\sqrt{27}+3\\sqrt{75}-9\\sqrt{48}$<br\/>$ =\\sqrt{3.4}+2.\\sqrt{3.9}+3.\\sqrt{3.25}-9.\\sqrt{3.16} $<br\/>$ =\\sqrt{3}.\\left( \\sqrt{4}+2\\sqrt{9}+3\\sqrt{25}-9\\sqrt{16} \\right) $<br\/>$ =\\sqrt{3}\\left( 2+6+15-36 \\right)$<br\/> $=-13\\sqrt{3} $<br\/><span class='basic_pink'>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 A <\/span><\/span>","column":2}]}],"id_ques":545},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[2]],"list":[{"point":5,"ques":"K\u1ebft qu\u1ea3 c\u1ee7a ph\u00e9p t\u00ednh $\\sqrt{4-2\\sqrt{3}}+\\sqrt{4+2\\sqrt{3}}$ l\u00e0: ","select":["A. $\\sqrt{3}$","B. $2\\sqrt{3}$ ","C. $-\\sqrt{3}$","D. $-2\\sqrt{3}$ "],"hint":"Bi\u1ebfn \u0111\u1ed5i bi\u1ec3u th\u1ee9c d\u01b0\u1edbi d\u1ea5u c\u0103n v\u1ec1 d\u1ea1ng $(A\\pm B)^2$ r\u1ed3i t\u00ednh","explain":"<span class='basic_left'> $\\sqrt{4-2\\sqrt{3}}+\\sqrt{4+2\\sqrt{3}} $<br\/>$ =\\sqrt{(\\sqrt{3})^2-2.\\sqrt{3}.1+{{1}^{2}}}\\,\\,$$+\\sqrt{(\\sqrt{3})^2+2.\\sqrt{3}.1+{{1}^{2}}} $<br\/>$\\begin{align}& =\\sqrt{{{\\left( \\sqrt{3}-1 \\right)}^{2}}}+\\sqrt{{{\\left( \\sqrt{3}+1 \\right)}^{2}}} \\\\ & =\\sqrt{3}-1+\\sqrt{3}+1 \\,\\,\\,\\,(V\u00ec \\,\\,\\sqrt{3}\\,>1)\\\\ & =2\\sqrt{3} \\\\ \\end{align}$<br\/><span class='basic_pink'>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 B <\/span><\/span>","column":2}]}],"id_ques":546},{"time":24,"part":[{"title":"Kh\u1eb3ng \u0111\u1ecbnh sau \u0110\u00fang hay Sai","title_trans":"","temp":"multiple_choice","correct":[[2]],"list":[{"point":5,"ques":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/daiso/bai3/lv2/img\/4.jpg' \/><\/center>V\u1edbi $a,b\\in \\mathbb N $ th\u00ec $\\sqrt{\\dfrac{{{b}^{2}}}{{{a}^{4}}}}=\\dfrac{b}{{{a}^{2}}}$ ","select":["A. \u0110\u00fang","B. Sai "],"hint":"","explain":"<span class='basic_left'>Ta c\u00f3: V\u00ec $a \\in \\mathbb N$ n\u00ean $a$ c\u00f3 th\u1ec3 b\u1eb1ng $0$<br\/>M\u00e0 $a$ l\u00e0 n\u1eb1m \u1edf m\u1eabu s\u1ed1. <br\/>Do \u0111\u00f3 kh\u1eb3ng \u0111\u1ecbnh tr\u00ean l\u00e0 Sai.<br\/><span class='basic_pink'>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 B <\/span>","column":2}]}],"id_ques":547},{"time":24,"part":[{"title":"Kh\u1eb3ng \u0111\u1ecbnh sau \u0110\u00fang hay Sai","title_trans":"","temp":"multiple_choice","correct":[[1]],"list":[{"point":5,"ques":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/daiso/bai3/lv2/img\/1.png' \/><\/center>V\u1edbi m\u1ecdi $a,b\\in \\mathbb R$ v\u00e0 $b> 0$ th\u00ec $\\sqrt{\\dfrac{{{a}^{4}}}{{{b}^{6}}}}=\\dfrac{{{a}^{2}}}{{{b}^{3}}}$ ","select":["A. \u0110\u00fang","B. Sai "],"hint":"","explain":"<span class='basic_left'>Ta c\u00f3:<br\/>$\\sqrt{\\dfrac{{{a}^{4}}}{{{b}^{6}}}}=\\dfrac{\\sqrt{{{a}^{4}}}}{\\sqrt{{{b}^{6}}}}=\\dfrac{{{a}^{2}}}{\\left| {{b}^{3}} \\right|}=\\dfrac{{{a}^{2}}}{{{b}^{3}}}$$\\,\\,\\,\\,\\,\\left(\\,\\,\\text{V\u00ec}\\,\\, b>0 \\right)$<br\/> Kh\u1eb3ng \u0111\u1ecbnh tr\u00ean l\u00e0 \u0110\u00fang .<br\/><span class='basic_pink'>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 A <\/span>","column":2}]}],"id_ques":548},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["11"]]],"list":[{"point":5,"width":40,"content":"","type_input":"","type_check":"","ques":"T\u00ednh $\\left( \\sqrt{125}+\\sqrt{245}-\\sqrt{5} \\right):\\sqrt{5}=$ _input_","hint":"Chia t\u1eebng s\u1ed1 h\u1ea1ng trong ngo\u1eb7c cho $\\sqrt 5$","explain":"<span class='basic_left'>Ta c\u00f3:<br\/>$\\begin{align} & \\left( \\sqrt{125}+\\sqrt{245}-\\sqrt{5} \\right):\\sqrt{5} \\\\ & =\\sqrt{25}+\\sqrt{49}-\\sqrt{1} \\\\ & =5+7-1 \\\\ & =11 \\\\ \\end{align}$ <br\/><span class='basic_pink'>V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u00e0 $11$ <\/span> <\/span>"}]}],"id_ques":549},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["0"]]],"list":[{"point":5,"width":40,"content":"","type_input":"","type_check":"","ques":"T\u00ednh $\\sqrt{12}-\\sqrt{27}+\\sqrt{3} =$_input_","hint":"T\u00e1ch m\u1ed7i s\u1ed1 d\u01b0\u1edbi d\u1ea5u c\u0103n v\u1ec1 d\u1ea1ng $a^2.b$ r\u1ed3i \u00e1p d\u1ee5ng: $\\sqrt{a^2b}=a\\sqrt b$","explain":"<span class='basic_left'>Ta c\u00f3:<br\/>$\\begin{align} & \\sqrt{12}-\\sqrt{27}+\\sqrt{3} \\\\ & =\\sqrt{3.4}-\\sqrt{9.3}+\\sqrt{3.1} \\\\ & =\\sqrt{3}.\\sqrt{4}-\\sqrt{9}.\\sqrt{3}+\\sqrt{3}.1 \\\\ & =2\\sqrt{3}-3\\sqrt{3}+\\sqrt{3} \\\\ & =0 \\\\ \\end{align}$ <br\/><span class='basic_pink'>V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u00e0 $0$ <\/span><\/span>"}]}],"id_ques":550}],"lesson":{"save":0,"level":2}}