\(\sqrt{3+2\sqrt{2}}-\sqrt{6-4\sqrt{2}}=\sqrt{\left(\sqrt{2}\right)^2+2.\sqrt{2}.1+1^2}-\sqrt{2^2-2.2.\sqrt{2}+\left(\sqrt{2}\right)^2}\)
= \(\sqrt{\left(\sqrt{2}+1\right)^2}-\sqrt{\left(2-\sqrt{2}\right)^2}=\sqrt{2}+1-2+\sqrt{2}\)
= \(2\sqrt{2}-1\)
Thực hiện các phép tính
a, \(\sqrt{5+2\sqrt{6}}-\sqrt{2-2\sqrt{6}}\)
b,\(\sqrt{7-2\sqrt{10}}-\sqrt{7+2\sqrt{10}}\)
c, \(\sqrt{4-2\sqrt{3}}+\sqrt{4+2\sqrt{3}}\)
d, \(\sqrt{24+8\sqrt{5}+}\sqrt{9-4\sqrt{5}}\)
tính :
A=\(\dfrac{\sqrt{2}+\sqrt{3}+\sqrt{6}+\sqrt{8}+4}{\sqrt{2}+\sqrt{3}+\sqrt{4}}\)
B=\(\sqrt{14+\sqrt{40}+\sqrt{56}+\sqrt{140}}\)
tính a) \(\sqrt[3]{2-\sqrt{5}}.\left(\sqrt[6]{9+4\sqrt{5}}+\sqrt[3]{2+\sqrt{5}}\right)\)
b) \(\sqrt[4]{17+12\sqrt{2}}-\sqrt{2}\)
c) \(\sqrt[4]{56-24\sqrt{5}}\)
d) \(1+\sqrt[4]{28-16\sqrt{3}}\)
e) \(\frac{2}{\sqrt{4-3\sqrt[4]{5}+2\sqrt{5}-\sqrt[4]{125}}}\)
@Akai Haruma giúp em với chị ơi
Rút gọn các biểu thức sau
a. \(\sqrt{3+2\sqrt{2}}-\sqrt{6-4\sqrt{2}}\)
b. \(\sqrt{9-4\sqrt{5}}-\sqrt{5}\)
c. \(\sqrt{23+8\sqrt{7}}-\sqrt{7}\)
\(\sqrt{3+2\sqrt{2}}-\sqrt{6-4\sqrt{2}}\) 
giải pt:
19+3x+4\(\sqrt{-x^2-x+6}\) = \(6\sqrt{x-2}+12\sqrt{3+x}\)
Rút gọn:
A=\(\dfrac{\sqrt{a}+2}{\sqrt{a+3}}-\dfrac{5}{a+\sqrt{a}-6}+\dfrac{1}{2-\sqrt{a}}\)
B=\((1-\dfrac{\sqrt{a}}{\sqrt{a}+1})\div(\dfrac{\sqrt{a}+3}{\sqrt{a}-2}+\dfrac{\sqrt{a}+2}{3-\sqrt{a}}+\dfrac{\sqrt{a}+2}{a-5\sqrt{a}+6)}\)
C=\((\dfrac{\sqrt{a}-1}{3\sqrt{a}-1}-\dfrac{1}{3\sqrt{a}+1}+\dfrac{8\sqrt{a}}{9a-1})\div(1-\dfrac{3\sqrt{a}-2}{3\sqrt{a}+1)}\)
Giups mình cái mình đag cần gấp
1. giải phương trình
a. \(\sqrt{x+4}=3\)
b. \(\sqrt{x-1}-\sqrt{9x-9}+2\sqrt{36x-36}=2+\sqrt{25x-25}\)
c. \(\sqrt{4x-20}+\sqrt{x-5}-\dfrac{1}{3}\cdot\sqrt{9x-45}=4\)
d.\(\sqrt{x^2-10x+25}=x-3\)
e. \(\sqrt{x^2-4x+4}=2\)
giải phương trình sau :
\(\sqrt{x}+\sqrt[4]{x\text{(}1-x\text{)}^2}+\sqrt[4]{\text{(}1-x\text{)}^3}=\sqrt{1-x}+\sqrt[4]{x^3}+\sqrt[4]{x^2.\text{(}1-x\text{)}}\)