\(=\sqrt{2}\left(\sqrt{3}-1\right)\sqrt{2+\sqrt{3}}\)
\(=\left(\sqrt{3}-1\right)\sqrt{4+2\sqrt{3}}\)
\(=\left(\sqrt{3}-1\right)\sqrt{\left(\sqrt{3}+1\right)^2}\)
\(=\left(\sqrt{3}-1\right)\left(\sqrt{3}+1\right)=2\)
Bài 1: Căn bậc hai
Các câu hỏi tương tự
Dleft ( frac{1}{3sqrt{x}-6} +frac{1}{x-2sqrt{x}}right )left ( frac{1}{6} +frac{1}{2sqrt{x}}right ) Dleft ( frac{1}{3left ( sqrt{x}-2 right )} +frac{1}{sqrt{x}left ( sqrt{x}-2 right )}right ).frac{sqrt{x}+3}{6sqrt{x}} Dfrac{sqrt{x}+3}{3sqrt{x}left ( sqrt{x}-2 right )}.frac{sqrt{x}+3}{6sqrt{x}} Dfrac{left ( sqrt{x}+3 right )^{2}}{18xleft ( sqrt{x}-2 right )} Dfrac{x+6sqrt{x}+9}{18xsqrt{x}-36x}
A/ Đúng
B/ Sai
Đọc tiếp
\[D=\left ( \frac{1}{3\sqrt{x}-6} +\frac{1}{x-2\sqrt{x}}\right )\left ( \frac{1}{6} +\frac{1}{2\sqrt{x}}\right )\\ D=\left ( \frac{1}{3\left ( \sqrt{x}-2 \right )} +\frac{1}{\sqrt{x}\left ( \sqrt{x}-2 \right )}\right ).\frac{\sqrt{x}+3}{6\sqrt{x}}\\ D=\frac{\sqrt{x}+3}{3\sqrt{x}\left ( \sqrt{x}-2 \right )}.\frac{\sqrt{x}+3}{6\sqrt{x}}\\ D=\frac{\left ( \sqrt{x}+3 \right )^{2}}{18x\left ( \sqrt{x}-2 \right )}\\ D=\frac{x+6\sqrt{x}+9}{18x\sqrt{x}-36x}\]
A/ Đúng
B/ Sai
Chứng minh rằng:
a)\(\frac{\left(5+2\sqrt{6}\right)\left(49-20\sqrt{6}\right)\left(\sqrt{5-2\sqrt{6}}\right)}{9\sqrt{3}-11\sqrt{2}}\) là số nguyên
b)\(\left(\sqrt{3}-1\right).\sqrt{6+2\sqrt{2}\sqrt{3-\sqrt{\sqrt{2}+\sqrt{12}+\sqrt{18-\sqrt{128}}}}}\)
\(\left(\dfrac{3}{2}\sqrt{6}+2\sqrt{\dfrac{2}{3}}-4\sqrt{\dfrac{3}{2}}\right)\times\left(3\sqrt{\dfrac{2}{3}}-\sqrt{2}-\sqrt{6}\right)\times\left(-\sqrt{6}\right)\)
16 tháng 10 2020 lúc 12:44
Rút gọn biểu thức \(\frac{\sqrt{6+2\left(\sqrt{6}+\sqrt{3}+\sqrt{2}\right)}-\sqrt{6-2\left(\sqrt{6}-\sqrt{3}+\sqrt{2}\right)}}{\sqrt{2}}\)
Tính:
E=(\(\sqrt{18}-3\sqrt{6}+\sqrt{2}\)) \(\sqrt{2}+6\sqrt{3}\)
G=\(\left(2\sqrt{2}-\sqrt{5}+\sqrt{18}\right)\).\(\left(\sqrt{50}+\sqrt{5}\right)\)
H=\(\dfrac{2+\sqrt{2}}{\sqrt{2}+1}\).\(\dfrac{2-\sqrt{2}}{\sqrt{2}-1}\)
rÚT GỌN: Gsqrt{3+sqrt{5}}+sqrt{7-3sqrt{6}}-sqrt{2}
chững minh : a) 2sqrt{2}left(sqrt{3}-2right)+left(1+2sqrt{2}right)^2-2sqrt[]{6}9
b)left(3+sqrt{5}right)left(sqrt{10}-sqrt{2}right)sqrt{3-sqrt{5}}8
c)sqrt{dfrac{4}{left(2-sqrt{5}right)^2}}-sqrt{dfrac{4}{left(2+sqrt{5}right)^2}}8
giúp mk với tối mai mk nạp rồi
Đọc tiếp
rÚT GỌN: G=\(\sqrt{3+\sqrt{5}}+\sqrt{7-3\sqrt{6}}-\sqrt{2}\)
chững minh : a) \(2\sqrt{2}\left(\sqrt{3}-2\right)+\left(1+2\sqrt{2}\right)^2-2\sqrt[]{6}=9\)
b)\(\left(3+\sqrt{5}\right)\left(\sqrt{10}-\sqrt{2}\right)\sqrt{3-\sqrt{5}}=8\)
c)\(\sqrt{\dfrac{4}{\left(2-\sqrt{5}\right)^2}}-\sqrt{\dfrac{4}{\left(2+\sqrt{5}\right)^2}}=8\)
giúp mk với tối mai mk nạp rồi
rút gọn M=\(\left(\sqrt{6}+\sqrt{2}\right)\left(\sqrt{3}-2\right)\sqrt{\sqrt{3}+2}\)
1. làm tính nhân :
a)left(sqrt{12}-3sqrt{75}right).sqrt{3}
b) left(sqrt{18}-4sqrt{72}right).2sqrt{2}
c) left(sqrt{6}-2right)left(sqrt{6}+7right)
d) left(sqrt{3}+2right)left(sqrt{3}-5right)
2) thực hien phep tinh :
a) left(sqrt{48}-sqrt{27}+4sqrt{12}right):sqrt{3}
b) left(sqrt{20}-3sqrt{45}+6sqrt{180}right):sqrt{5}
c) left(2sqrt{20}-3sqrt{45}+4sqrt{80}right):sqrt{5}
d) left(3sqrt{24}+4sqrt{54}-5sqrt{96}right):sqrt{6}
e)left(sqrt{x^2y}-sqrt{xy^2}right):sqrt{xy}
f) left(sqrt{a^3b}+sqrt...
Đọc tiếp
1. làm tính nhân :
a)\(\left(\sqrt{12}-3\sqrt{75}\right).\sqrt{3}\)
b) \(\left(\sqrt{18}-4\sqrt{72}\right).2\sqrt{2}\)
c) \(\left(\sqrt{6}-2\right)\left(\sqrt{6}+7\right)\)
d) \(\left(\sqrt{3}+2\right)\left(\sqrt{3}-5\right)\)
2) thực hien phep tinh :
a) \(\left(\sqrt{48}-\sqrt{27}+4\sqrt{12}\right):\sqrt{3}\)
b) \(\left(\sqrt{20}-3\sqrt{45}+6\sqrt{180}\right):\sqrt{5}\)
c) \(\left(2\sqrt{20}-3\sqrt{45}+4\sqrt{80}\right):\sqrt{5}\)
d) \(\left(3\sqrt{24}+4\sqrt{54}-5\sqrt{96}\right):\sqrt{6}\)
e)\(\left(\sqrt{x^2y}-\sqrt{xy^2}\right):\sqrt{xy}\)
f) \(\left(\sqrt{a^3b}+\sqrt{ab^3}-ab\right):\sqrt{ab}\)
g) \(\left(3\sqrt{x^2y}-4\sqrt{xy^2}+5xy\right):\sqrt{xy}\)
h) \(\left(\sqrt{a^3b}+\sqrt{ab^3-3\sqrt{ab}}\right):\sqrt{ab}\)
\(\sqrt{15-\sqrt{216}}+\sqrt{33-12\sqrt{6}}\)
= \(\sqrt{\left(3-\sqrt{6}\right)^2}+\sqrt{\left(3-2\sqrt{6}\right)^2}\)
= \(3-\sqrt{6}+3-2\sqrt{6}\)
Rút gọn căn bậc hai theo hằng đẳng thức:
a)left(4sqrt{2}+sqrt{30}right).left(sqrt{5}-sqrt{3}right)sqrt{4-sqrt{15}}
b)2.left(sqrt{10}-sqrt{2}right).left(4+sqrt{6-2sqrt{5}}right)
c)left(7+sqrt{14}right).sqrt{9-2sqrt{14}}
d)sqrt{dfrac{289+4sqrt{72}}{16}}
e) left(sqrt{21}+7right).sqrt{10-2sqrt{21}}
f)sqrt{2-sqrt{3}.left(sqrt{6}+sqrt{2}right)}
g) sqrt{2}sqrt{8+3sqrt{7}}
h) sqrt{11+6sqrt{2}}
Đọc tiếp
Rút gọn căn bậc hai theo hằng đẳng thức:
a)\(\left(4\sqrt{2}+\sqrt{30}\right).\left(\sqrt{5}-\sqrt{3}\right)\sqrt{4-\sqrt{15}}\)
b)\(2.\left(\sqrt{10}-\sqrt{2}\right).\left(4+\sqrt{6-2\sqrt{5}}\right)\)
c)\(\left(7+\sqrt{14}\right).\sqrt{9-2\sqrt{14}}\)
d)\(\sqrt{\dfrac{289+4\sqrt{72}}{16}}\)
e) \(\left(\sqrt{21}+7\right).\sqrt{10-2\sqrt{21}}\)
f)\(\sqrt{2-\sqrt{3}.\left(\sqrt{6}+\sqrt{2}\right)}\)
g) \(\sqrt{2}\sqrt{8+3\sqrt{7}}\)
h) \(\sqrt{11+6\sqrt{2}}\)