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) \(\sqrt{\frac{-x^2-1}{x-3}}\)
\(a,=5\sqrt{5}-12\sqrt{5}+6\sqrt{5}-4\sqrt{5}=-5\sqrt{5}\)
\(\sqrt{29^2-20^2}=\sqrt{\left(29-20\right)\left(29+20\right)}=\sqrt{3^2.7^2}=21\)
\(\text{Đặt: }\)\(\hept{\begin{cases}\sqrt{4-\sqrt{15}}=a\\\sqrt{4+\sqrt{15}}=b\end{cases}}\)\(\text{cần tính: a-b}\)
\(\hept{\begin{cases}ab=\sqrt{\left(4-\sqrt{15}\right)\left(4+\sqrt{15}\right)}=1\\a^2+b^2=8\end{cases}}\Rightarrow\left(a-b\right)^2=6\Rightarrow a-b=-\sqrt{6}\left(vì:a< b\right)\)
\(\sqrt{29^2-20^2}=\sqrt{9.49}=\sqrt{\left(3.7\right)^2}=21\)
\(3.\sqrt{2}.\left(\sqrt{50}-2\sqrt{18}+\sqrt{98}\right)=3.\left(\sqrt{100}-2.\sqrt{36}+\sqrt{196}\right)=3.\left(10-2.6+14\right)=3.16=48\)\(A^2=\left(\sqrt{4-\sqrt{15}}-\sqrt{4+\sqrt{15}}\right)^2=8-2.\sqrt{\left(4-\sqrt{15}\right)\left(4+\sqrt{15}\right)}=8-2=6\)
Bài 2 :
1) ĐKXĐ:\(-x^2-5\ge0\)
\(\Leftrightarrow x^2+5\le0\)
Mặt khác \(x^2+5\ge0\forall x\)
Do đó biểu thức không xác định với mọi x
2) ĐKXĐ:\(x-4\ge0\)
\(\Leftrightarrow x\ge4\)
3) ĐKXĐ:\(\frac{-3}{x+1}\ge0\)( \(x\ne-1\))
\(\Leftrightarrow x+1< 0\)
\(\Leftrightarrow x< -1\)
4) ĐKXĐ:\(\frac{-x^2-1}{x-3}\ge0\)( \(x\ne3\))
\(\Leftrightarrow\frac{x^2+1}{3-x}\ge0\)
Mà \(x^2+1>0\forall x\)
\(\Rightarrow3-x>0\)
\(\Leftrightarrow x< 3\)
