Question

[dangvuhoaianh]

Bài 1: Tính

a) \(\sqrt{125}-4\sqrt{45}+3\sqrt{20}-\sqrt{80}\)

b) \(\sqrt{29^2-20^2}\)

c) \(3\sqrt{2}\left(\sqrt{50}-2\sqrt{18}+\sqrt{98}\right)\)

d) \(\sqrt{4-\sqrt{15}}-\sqrt{4+\sqrt{15}}\)

e) \(\sqrt{3-\sqrt{5}}\left(3+\sqrt{5}\right)\cdot\left(\sqrt{10}-\sqrt{2}\right)\)

f) \(2\sqrt{5}-\sqrt{125}-\sqrt{80}+\sqrt{605}\)

g) \(\sqrt{3}-3\sqrt{12}+4\sqrt{27}+3\)

Bài 2: Tìm ĐKXĐ

1) \(\sqrt{-x^2-5}\)

2) \(\frac{\sqrt{x-4}}{3}\)

3) \(\sqrt{\frac{-3}{x+1}}\)

4) \(\sqrt{\frac{-x^2-1}{x-3}}\)

Answer 1

[shitbo]

\(a,=5\sqrt{5}-12\sqrt{5}+6\sqrt{5}-4\sqrt{5}=-5\sqrt{5}\)

\(\sqrt{29^2-20^2}=\sqrt{\left(29-20\right)\left(29+20\right)}=\sqrt{3^2.7^2}=21\)

Answer 2

[shitbo]

\(\text{Đặt: }\)\(\hept{\begin{cases}\sqrt{4-\sqrt{15}}=a\\\sqrt{4+\sqrt{15}}=b\end{cases}}\)\(\text{cần tính: a-b}\)

\(\hept{\begin{cases}ab=\sqrt{\left(4-\sqrt{15}\right)\left(4+\sqrt{15}\right)}=1\\a^2+b^2=8\end{cases}}\Rightarrow\left(a-b\right)^2=6\Rightarrow a-b=-\sqrt{6}\left(vì:a< b\right)\)