thực hiện phép tính :
a) A=\(\sqrt{12-3\sqrt{7}}-\sqrt{12+3\sqrt{7}}\)
b) B =\(\sqrt{4+\sqrt{10+2\sqrt{5}}}+\sqrt{4-\sqrt{10+2\sqrt{5}}}\)
c) C =\(\sqrt{3-\sqrt{5}}+\sqrt{3+\sqrt{5}}\)
giúp mjk bài này với :) mjk đang cần gấp lắm
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12 tháng 10 2021 lúc 19:48
* Thực hiện phép tính
a, A= \(\sqrt{12-3\sqrt{7}}-\sqrt{12+3\sqrt{7}}\)
b, B= \(\sqrt{4+\sqrt{10+2\sqrt{5}}}+\sqrt{4-\sqrt{10+2\sqrt{5}}}\)
c, C= \(\sqrt{3-\sqrt{5}}+\sqrt{3+\sqrt{5}}\)
c: Ta có: \(C=\sqrt{3-\sqrt{5}}+\sqrt{3+\sqrt{5}}\)
\(=\dfrac{\sqrt{6-2\sqrt{5}}+\sqrt{6+2\sqrt{5}}}{\sqrt{2}}\)
\(=\dfrac{\sqrt{5}-1+\sqrt{5}+1}{\sqrt{2}}=\sqrt{10}\)
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Thực hiện các phép tính sau:
a, A=\(\sqrt{12-3\sqrt{7}}-\sqrt{12+3\sqrt{7}}\)
b, B=\(\sqrt{4+\sqrt{10+2\sqrt{5}}}+\sqrt{4-\sqrt{10+2\sqrt{5}}}\)
c, C=\(\sqrt{3-\sqrt{5}}+\sqrt{3+\sqrt{5}}\)
a, A= \(\frac{\sqrt{48-12\sqrt{7}}}{2}-\frac{\sqrt{48+12\sqrt{7}}}{2}\)
= \(\frac{\sqrt{\left(\sqrt{42}-\sqrt{6}\right)^2}}{2}-\frac{\sqrt{\left(\sqrt{42}+\sqrt{6}\right)^2}}{2}\)
= \(\frac{-2\sqrt{6}}{2}\)
= \(-\sqrt{6}\)
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1/ thực hiện phép tính:
a) (\(\sqrt{4+2\sqrt{3}}-\sqrt{4-2\sqrt{3}}\)) . (\(\sqrt{4-2\sqrt{3}}+\sqrt{4+2\sqrt{3}}\))
b) ( \(\sqrt{4+\sqrt{7}}-\sqrt{4-\sqrt{7}}\))2
c) \(\sqrt{5-\sqrt{3-\sqrt{29-12\sqrt{5}}}}\)
giúp mjk nha m.n!! thks nhìu
a.\(\left(\sqrt{4+2\sqrt{3}}-\sqrt{4-2\sqrt{3}}\right).\left(\sqrt{4-2\sqrt{3}}+\sqrt{4+2\sqrt{3}}\right)\)
\(=\left(\sqrt{\left(\sqrt{3}+1\right)^2}-\sqrt{\left(\sqrt{3}-1\right)^2}\right).\left(\sqrt{\left(\sqrt{3}-1\right)^2}+\sqrt{\left(\sqrt{3}+1\right)^2}\right)\)
\(=\left(\sqrt{3}+1-\sqrt{3}+1\right)\left(\sqrt{3}-1+\sqrt{3}+1\right)\)
\(=2.2\sqrt{3}=4\sqrt{3}\)
b.\(\left(\sqrt{4+\sqrt{7}}-\sqrt{4-\sqrt{7}}\right)^2=\left[\frac{\sqrt{8+2\sqrt{7}}}{\sqrt{2}}-\frac{\sqrt{8-2\sqrt{7}}}{\sqrt{2}}\right]^2\)
\(=\left(\frac{\sqrt{\left(\sqrt{7}+1\right)^2}}{\sqrt{2}}-\frac{\sqrt{\left(\sqrt{7}-1\right)^2}}{\sqrt{2}}\right)^2\)
\(=\left(\frac{\sqrt{7}+1-\sqrt{7}+1}{\sqrt{2}}\right)^2=\left(\sqrt{2}\right)^2=2\)
c.\(\sqrt{5-\sqrt{3-\sqrt{29-12\sqrt{5}}}}=\sqrt{5-\sqrt{3-\sqrt{\left(2\sqrt{5}-3\right)^2}}}\)
\(=\sqrt{5-\sqrt{3-\left(2\sqrt{5}-3\right)}}=\sqrt{5-\sqrt{6-2\sqrt{5}}}\)
\(=\sqrt{5-\sqrt{\left(\sqrt{5}-1\right)^2}}=\sqrt{5-\sqrt{5}+1}=\sqrt{6-\sqrt{5}}\)
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\(A=\sqrt{12-3\sqrt{7}}-\sqrt{12+3\sqrt{7}}\)
\(B=\sqrt{4+\sqrt{10+2\sqrt{5}}}+\sqrt{4-\sqrt{10+2\sqrt{5}}}\)\(C=\sqrt{3-\sqrt{5}}+\sqrt{3+\sqrt{5}}\)
Bài 1: Thực hiện các phép tính
a) A= \(\sqrt{12-2\sqrt{7}}-\sqrt{12+2\sqrt{7}}\)
b) B= \(\sqrt{4+\sqrt{10+2\sqrt{5}}}+\sqrt{4-\sqrt{10+2\sqrt{5}}}\)
c) C= \(\sqrt{3-\sqrt{5}}+\sqrt{3+\sqrt{5}}\)
a: \(A^2=12-2\sqrt{7}+12+2\sqrt{7}-2\cdot\sqrt{116}\)
\(\Leftrightarrow A^2=24-4\sqrt{29}\)
hay \(A=\sqrt{24-4\sqrt{29}}\)
c: \(C=\dfrac{\sqrt{6-2\sqrt{5}}+\sqrt{6+2\sqrt{5}}}{\sqrt{2}}\)
\(=\dfrac{\sqrt{5}-1+\sqrt{5}+1}{\sqrt{2}}=\dfrac{2\sqrt{5}}{\sqrt{2}}=\sqrt{10}\)
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Thực hiện phép tính:
a) \(\sqrt{12-3\sqrt{7}}-\sqrt{12+3\sqrt{7}}\)
b) \(\sqrt{4+\sqrt{10+2\sqrt{5}}}+\sqrt{4-\sqrt{10+2\sqrt{5}}}\)
c) \(\sqrt{3-\sqrt{5}}+\sqrt{3+\sqrt{5}}\)
c)\(\sqrt{3-\sqrt{5}}+\sqrt{3+\sqrt{5}}=\sqrt{3+\sqrt{5}}+\sqrt{3-\sqrt{5}}=A\\ \Rightarrow\sqrt{2}A=\sqrt{6+2\sqrt{5}+}\sqrt{6-\sqrt{5}}=\sqrt{\left(\sqrt{5}+1\right)^2}+\sqrt{\left(\sqrt{5}-1\right)^2}\\ =\sqrt{5}+1+\sqrt{5}-1\\ =2\sqrt{5}\\ \Rightarrow A=\sqrt{2}.\sqrt{5}=\sqrt{10}\)
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Thực hiện phép tính rút gọn sau:
\(A=\sqrt{8}-2\sqrt{18}+3\sqrt{50}\)
\(B=\sqrt{125}-10\sqrt{\dfrac{1}{20}}-\dfrac{\sqrt{5}-5}{\sqrt{5}}\)
\(C=\dfrac{1}{\sqrt{3}+\sqrt{2}}+\sqrt{7-4\sqrt{3}}+\sqrt{2}\)
a: Ta có: \(A=\sqrt{8}-2\sqrt{18}+3\sqrt{50}\)
\(=2\sqrt{2}-6\sqrt{2}+15\sqrt{2}\)
\(=11\sqrt{2}\)
b: Ta có: \(B=\sqrt{125}-10\sqrt{\dfrac{1}{20}}+\dfrac{5-\sqrt{5}}{\sqrt{5}}\)
\(=5\sqrt{5}-\sqrt{5}+\sqrt{5}-1\)
\(=5\sqrt{5}-1\)
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thực hiện phép tínha, dfrac{sqrt{3-sqrt{5}}.left(3+sqrt{5}right)}{sqrt{10}+sqrt{2}}b, sqrt{8sqrt{3}}-2sqrt{25sqrt{12}}+4sqrt{sqrt{192}}c, sqrt{2-sqrt{3}}.left(sqrt{5}+sqrt{2}right)d, sqrt{3-sqrt{5}}+sqrt{3+sqrt{5}}e, sqrt{4+sqrt{10+2sqrt{5}}}+sqrt{4-sqrt{10+2sqrt{5}}}f, left(5+2sqrt{6}right)left(49-20sqrt{6}right)sqrt{5-2sqrt{6}}g, dfrac{1}{sqrt{2}+sqrt{2+sqrt{3}}}+dfrac{1}{sqrt{2}-sqrt{2-sqrt{3}}}h, dfrac{6+4sqrt{2}}{sqrt{2}+sqrt{6+4sqrt{2}}}+dfrac{6-4sqrt{2}}{sqrt{2}+sqrt{6+4sqrt{2}}}i, dfrac{...
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thực hiện phép tính
a, \(\dfrac{\sqrt{3-\sqrt{5}}.\left(3+\sqrt{5}\right)}{\sqrt{10}+\sqrt{2}}\)
b, \(\sqrt{8\sqrt{3}}-2\sqrt{25\sqrt{12}}+4\sqrt{\sqrt{192}}\)
c, \(\sqrt{2-\sqrt{3}}.\left(\sqrt{5}+\sqrt{2}\right)\)
d, \(\sqrt{3-\sqrt{5}}+\sqrt{3+\sqrt{5}}\)
e, \(\sqrt{4+\sqrt{10+2\sqrt{5}}}+\sqrt{4-\sqrt{10+2\sqrt{5}}}\)
f, \(\left(5+2\sqrt{6}\right)\left(49-20\sqrt{6}\right)\sqrt{5-2\sqrt{6}}\)
g, \(\dfrac{1}{\sqrt{2}+\sqrt{2+\sqrt{3}}}+\dfrac{1}{\sqrt{2}-\sqrt{2-\sqrt{3}}}\)
h, \(\dfrac{6+4\sqrt{2}}{\sqrt{2}+\sqrt{6+4\sqrt{2}}}+\dfrac{6-4\sqrt{2}}{\sqrt{2}+\sqrt{6+4\sqrt{2}}}\)
i, \(\dfrac{\left(\sqrt{5+2}\right)^2-8\sqrt{5}}{2\sqrt{5}-4}\)
k, \(\sqrt{14-8\sqrt{3}}-\sqrt{24-12\sqrt{3}}\)
l, \(\dfrac{4}{\sqrt{3}+1}+\dfrac{1}{\sqrt{3}-2}+\dfrac{6}{\sqrt{3}-3}\)
m, \(\left(\sqrt{2}+1\right)^3-\left(\sqrt{2}-1\right)^3\)
n, \(\dfrac{\sqrt{3}}{1-\sqrt{\sqrt{3+1}}}+\dfrac{\sqrt{3}}{1+\sqrt{\sqrt{3+1}}}\)
1) thực hiện phép tính:
a) \(\dfrac{4}{\sqrt{7}-\sqrt{3}}+\dfrac{6}{3+\sqrt{3}}+\dfrac{\sqrt{7}-7}{\sqrt{7}-1}\)
b) \(\sqrt{4+\sqrt{10+2\sqrt{5}}}+\sqrt{4-\sqrt{10+2\sqrt{5}}}\)
giúp mk vs ah mk đang cần gấp lắm
a: Ta có: \(\dfrac{4}{\sqrt{7}-\sqrt{3}}+\dfrac{6}{3+\sqrt{3}}+\dfrac{\sqrt{7}-7}{\sqrt{7}-1}\)
\(=\sqrt{7}+\sqrt{3}+3-\sqrt{3}-\sqrt{7}\)
=3
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