Question

Rút gọn:

a)\(\sqrt{\left(\sqrt{7-2}\right)^2}\)

b)\(\sqrt{\left(\sqrt{2}-1\right)^2}-\sqrt{\left(2-3\sqrt{2}\right)^2}\)

c)\(\sqrt{4+2\sqrt{3}}+\sqrt{4-2\sqrt{3}}\)

d) \(\sqrt{2+\sqrt{3}}+\sqrt{2a-3}\)

e)\(\sqrt{\dfrac{2+\sqrt{3}}{2-\sqrt{3}}}+\sqrt{\dfrac{2-\sqrt{3}}{2+\sqrt{3}}}\)

f)\(\sqrt{9a^{ }2}+3a-7\left(v\text{ơ}\text{í}a< 0\right)\)

g) \(\dfrac{\sqrt{4x^2-4x+1}}{4x-2}+3x+2\)(vơí x>\(\dfrac{1}{2}\))

h)\(\sqrt{\left(5a-1\right)^2}+2a-3\)

i)\(\sqrt{\dfrac{2a}{5}}.\sqrt{\dfrac{5a}{18}+}2\left(a-1\right)\)(vơí a>=0)

Answer 1

a) \(\sqrt{\left(\sqrt{7-2}\right)^2}=\sqrt{5}\)

b)\(\sqrt{\left(\sqrt{2}-1\right)^2}-\sqrt{\left(2-3\sqrt{2}\right)^2}\)

=\(\sqrt{2}-1-2+3\sqrt{2}=4\sqrt{2}-3\)

c)\(\sqrt{4+2\sqrt{3}}+\sqrt{4-2\sqrt{3}}\)

=\(\sqrt{\left(\sqrt{3}+1\right)^2}+\sqrt{\left(\sqrt{3}-1\right)^2}=2\sqrt{3}\)

d) hình như bn ghi sai

e)\(\sqrt{\dfrac{2+\sqrt{3}}{2-\sqrt{3}}}+\sqrt{\dfrac{2-\sqrt{3}}{2+\sqrt{3}}}\)

=\(\left(\dfrac{\sqrt{2+\sqrt{3}}}{\sqrt{4-2\sqrt{3}}}+\dfrac{\sqrt{2-\sqrt{3}}}{\sqrt{4+2\sqrt{3}}}\right):\sqrt{2}\)

=\(\left(\dfrac{\sqrt{2+\sqrt{3}}}{\sqrt{3}-1}+\dfrac{\sqrt{2-\sqrt{3}}}{\sqrt{3}+1}\right):\sqrt{2}\)

=\(\dfrac{\sqrt{2+\sqrt{3}}\left(\sqrt{3}+1\right)+\sqrt{2-\sqrt{3}}\left(\sqrt{3}-1\right)}{2\sqrt{2}}\)

=\(\dfrac{\sqrt{6+3}+\sqrt{2+\sqrt{3}}+\sqrt{6-3}-\sqrt{2+\sqrt{3}}}{2\sqrt{2}}\)

=\(\dfrac{3+\sqrt{2+\sqrt{3}}+\sqrt{3}-\sqrt{2+\sqrt{3}}}{2\sqrt{2}}\)

=\(\dfrac{3+\sqrt{3}}{2\sqrt{2}}\)

f) \(\sqrt{9a^2}+3a-7=-3a+3a-7=-7\)

g)\(\dfrac{\sqrt{4x^2-4x+1}}{4x-2}+3x+2\)

=\(\dfrac{\sqrt{\left(2x-1\right)^2}}{4x-2}+3x+2=\dfrac{2x-1}{2\left(2x-1\right)}+3x+2\)

=\(\dfrac{1}{2}+3x+2=\dfrac{5}{2}+3x\)

h)\(\sqrt{\left(5a-1\right)^2}+2a-3\)

nếu a<0 :\(-5a+1+2a-3=-3a-2\)

nếu a>0 : \(5a-1+2a-3=7a-4\)

i)\(\sqrt{\dfrac{2a}{5}}.\sqrt{\dfrac{5a}{18}}+2\left(a-1\right)\)

=\(\sqrt{\dfrac{10a^2}{90}}+2a-2=\sqrt{\dfrac{a^2}{9}}+2a-2\)

=\(\dfrac{a}{3}+2a-2=\dfrac{7a}{3}-2\)