a: \(=\sqrt[3]{\dfrac{5}{625}}=\sqrt[3]{\dfrac{1}{125}}=\dfrac{1}{5}\)

b: \(=\sqrt[5]{\left(-\sqrt{5}\right)^5}=-\sqrt{5}\)

a, \(=>3-\sqrt{2}+\sqrt{50}=3-\sqrt{2}+5\sqrt{2}=3+4\sqrt{2}\)

b, \(=>\dfrac{\sqrt[3]{125.5}}{\sqrt[3]{5}}-\sqrt[3]{\left(-4\right).2}=\sqrt[3]{125}-\sqrt[3]{\left(-2\right)^3}\)

\(=5-\left(-2\right)=7\)

c, \(=>\sqrt{6}.\sqrt{\dfrac{6}{2}}-\sqrt{2}-3\sqrt{4.2}=\sqrt{6}.\sqrt{3}-\sqrt{2}-6\sqrt{2}\)

\(=\sqrt{18}-7\sqrt{2}=3\sqrt{2}-7\sqrt{2}=-4\sqrt{2}\)

d, \(=>\dfrac{\sqrt{3}\left(\sqrt{2}-1\right)}{\sqrt{2}-1}-\dfrac{2}{\sqrt{3}-1}=\sqrt{3}-\dfrac{2}{\sqrt{3}-1}\)

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

\(\sqrt[3]{216}.\sqrt{9025}.\sqrt[3]{125}+\sqrt{625}.\)

\(=\sqrt[3]{6^3}.\sqrt{95^2}.\sqrt[3]{5^3}+\sqrt{25^2}\)

\(=6.95.5+25\)

\(=2850+25=2875\)

Bạn bấm máy tính là ra

Bài 1:

a: ĐKXĐ: \(\frac{x^2}{2x-1}\ge0\)

=>2x-1>0

=>2x>1

=>\(x>\frac12\)

b: \(\frac{\sqrt[3]{625}}{\sqrt[3]{5}}-\sqrt[3]{-216}\cdot\sqrt[3]{\frac{1}{27}}\)

\(=\sqrt[3]{\frac{625}{5}}-\left(-6\right)\cdot\frac13=5+2=7\)

Bài 2:

a: \(\sqrt{\left(x+1\right)^2}=3\)

=>|x+1|=3

=>\(\left[\begin{array}{l}x+1=3\\ x+1=-3\end{array}\right.\Rightarrow\left[\begin{array}{l}x=2\\ x=-4\end{array}\right.\)

b: ĐKXĐ: x>=-1

\(3\sqrt{4x+4}-\sqrt{9x+9}-8\cdot\sqrt{\frac{x+1}{16}}=5\)

=>\(3\cdot2\cdot\sqrt{x+1}-3\sqrt{x+1}-8\cdot\frac{\sqrt{x+1}}{4}=5\)

=>\(3\sqrt{x+1}-2\sqrt{x+1}=5\)

=>\(\sqrt{x+1}=5\)

=>x+1=25

=>x=24(nhận)