a: \(\sqrt{5\left(1-a\right)^2}\)
\(=\sqrt{5\left(a-1\right)^2}\)
\(=\sqrt{5}\cdot\sqrt{\left(a-1\right)^2}\)
\(=\sqrt{5}\left|a-1\right|\)
\(=\sqrt{5}\left(a-1\right)\)(do a>1 nên a-1>0)
b: \(\sqrt{\dfrac{9\left|a^2+2a+1\right|}{144}}\)
\(=\sqrt{\dfrac{9}{144}\cdot\left|a^2+2a+1\right|}\)
\(=\sqrt{\dfrac{1}{16}\cdot\left|\left(a+1\right)^2\right|}\)
\(=\sqrt{\dfrac{1}{16}}\cdot\sqrt{\left|\left(a+1\right)^2\right|}\)
\(=\dfrac{1}{4}\cdot\left(a+1\right)^2\)
c:
ĐKXĐ: x<>5
Sửa đề:\(\dfrac{2}{x-5}\cdot\sqrt{\dfrac{x^2-10x+25}{64}}\)
\(=\dfrac{2}{x-5}\cdot\sqrt{\dfrac{\left(x-5\right)^2}{64}}\)
\(=\dfrac{2}{x-5}\cdot\dfrac{\sqrt{\left(x-5\right)^2}}{\sqrt{64}}\)
\(=\dfrac{2}{x-5}\cdot\dfrac{\left|x-5\right|}{8}\)
\(=\pm\dfrac{1}{4}\)
d: \(\dfrac{x-\sqrt{x}}{\sqrt{x}-1}\)
\(=\dfrac{\sqrt{x}\cdot\sqrt{x}-\sqrt{x}\cdot1}{\sqrt{x}-1}\)
\(=\dfrac{\sqrt{x}\left(\sqrt{x}-1\right)}{\sqrt{x}-1}=\sqrt{x}\)
