Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
a)\(3\sqrt{2}-\sqrt{8}+\sqrt{50}-4\sqrt{32}=3\sqrt{2}-2\sqrt{2}+5\sqrt{2}-16\sqrt{2}=-10\sqrt{2}\)
b) \(5\sqrt{48}-4\sqrt{27}-2\sqrt{75}+\sqrt{108}=20\sqrt{3}-12\sqrt{3}-10\sqrt{3}+6\sqrt{3}=4\sqrt{3}\)
c)\(\sqrt{12}+2\sqrt{75}-3\sqrt{48}-\frac{2}{7}\sqrt{147}=2\sqrt{3}+10\sqrt{3}-12\sqrt{3}-2\sqrt{3}=-2\sqrt{3}\)
d) \(\sqrt{\left(3+\sqrt{5}\right)^2}-\sqrt{9-4\sqrt{5}}\)
\(=\left|3+\sqrt{5}\right|-\sqrt{\left(\sqrt{5}-2\right)^2}=3+\sqrt{5}-\left|\sqrt{5}-2\right|=3+\sqrt{5}-\sqrt{5}+2=5\)
e) \(\left(\frac{\sqrt{6}-\sqrt{2}}{1-\sqrt{3}}-\frac{5}{\sqrt{5}}\right):\frac{\sqrt{5}+\sqrt{2}}{3}\)
\(=\left[\frac{\sqrt{2}\left(\sqrt{3}-1\right)}{1-\sqrt{3}}-\sqrt{5}\right]\cdot\frac{3}{\sqrt{5}+\sqrt{2}}\)
\(=-\left(\sqrt{2}+\sqrt{5}\right)\cdot\frac{3}{\sqrt{5}+\sqrt{2}}=-3\)
Nản k lm nữa ^^
a) \(\sqrt{17}-4\) b) \(\sqrt{3}\) c) \(\frac{\sqrt{2}}{2}\) d)\(\frac{\sqrt{x}+1}{\sqrt{x}-1}\) e) \(x-\sqrt{5}\)
f) \(4+2\sqrt{3}\) g) \(3+2\sqrt{2}\) h) \(x+\sqrt{x}+1\) i) \(\frac{3\sqrt{5}-\sqrt{15}}{10}\)
k) \(\sqrt{5}+\sqrt{6}\) i) 5 h) 0 l) \(\sqrt{5}+\sqrt{3}\) m) \(\frac{20\sqrt{3}}{3}\) d) 0
1, \(=\frac{4\sqrt{2}\left(2-\sqrt{2}\right)}{2^2-\sqrt{2}^2}-\frac{4\sqrt{2}\left(2+\sqrt{2}\right)}{2^2-\sqrt{2}^2}\)
=\(\frac{4\sqrt{2}\left(2-\sqrt{2}\right)}{2}-\frac{4\sqrt{2}\left(2+\sqrt{2}\right)}{2}\)
=\(2\sqrt{2}\left(2-\sqrt{2}\right)-2\sqrt{2}\left(2+\sqrt{2}\right)\)
=\(4\sqrt{2}-4-4\sqrt{2}-4\)
=-8
2, =\(\sqrt{2}+\sqrt{2}-2.3\sqrt{2}+\left|1-\sqrt{2}\right|\)
= \(-4\sqrt{2}+1-\sqrt{2}\) = \(1-5\sqrt{2}\)
3, =\(9\sqrt{\frac{2.2}{3.2}}+5\sqrt{9.6}-\sqrt{\frac{1}{6}}\)
=\(3\sqrt{6}+15\sqrt{6}-\frac{1}{6}\sqrt{6}\)
=\(\frac{107}{6}\sqrt{6}\)
4, =\(\sqrt{\left(4+2\sqrt{2}\right)\left(4-2\sqrt{2}\right)}.\left(2\sqrt{2}-\sqrt{2}\right)\)
= \(\sqrt{4^2-\left(2\sqrt{2}\right)^2}.\sqrt{2}\)
= \(\sqrt{16-8}.\sqrt{2}\)
= \(\sqrt{8}.\sqrt{2}=\sqrt{16}=4\)
5, = \(\sqrt{9-2.3.\sqrt{5}+5}+\sqrt{1-2.1.\sqrt{2}+2}+\sqrt{5-2.\sqrt{2}.\sqrt{5}+2}\)
\(=\sqrt{\left(3-\sqrt{5}\right)^2}+\sqrt{(1-\sqrt{2})^2}+\sqrt{\left(\sqrt{5}-\sqrt{2}\right)^2}\)\(=\left|3-\sqrt{5}\right|+\left|1-\sqrt{2}\right|+\left|\sqrt{5}-\sqrt{2}\right|\)
\(=3-\sqrt{5}+1-\sqrt{2}+\sqrt{5}-\sqrt{2}\)
\(=4-2\sqrt{2}\)
b) \(B=\frac{\sqrt{2}+\sqrt{3}+\sqrt{6}+\sqrt{8}+4}{\sqrt{2}+\sqrt{3}+\sqrt{4}}\)
\(=\frac{\sqrt{2}+\sqrt{3}+\sqrt{6}+\sqrt{8}+2+2}{\sqrt{2}+\sqrt{3}+\sqrt{4}}\)
\(=\frac{\sqrt{2}+\sqrt{3}+\sqrt{4}+\sqrt{4}+\sqrt{6}+\sqrt{8}}{\sqrt{2}+\sqrt{3}+\sqrt{4}}\)
\(=\frac{\left(\sqrt{2}+\sqrt{3}+\sqrt{4}\right)+\left(\sqrt{4}+\sqrt{6}+\sqrt{8}\right)}{\sqrt{2}+\sqrt{3}+\sqrt{4}}\)
\(=\frac{\left(\sqrt{2}+\sqrt{3}+\sqrt{4}\right)+\sqrt{2}.\left(\sqrt{2}+\sqrt{3}+\sqrt{4}\right)}{\sqrt{2}+\sqrt{3}+\sqrt{4}}\)
\(=\frac{\left(\sqrt{2}+\sqrt{3}+\sqrt{4}\right)\left(\sqrt{2}+1\right)}{\sqrt{2}+\sqrt{3}+\sqrt{4}}=\sqrt{2}+1\)
c) \(C=\sqrt{3+2\sqrt{2}}+\sqrt{6-4\sqrt{2}}\)
\(=\sqrt{2+2\sqrt{2}+1}+\sqrt{4-4\sqrt{2}+2}\)
\(=\sqrt{\left(\sqrt{2}+1\right)^2}+\sqrt{\left(2-\sqrt{2}\right)^2}\)
\(=\left|\sqrt{2}+1\right|+\left|2-\sqrt{2}\right|\)
\(=\sqrt{2}+1+2-\sqrt{2}=3\)