Question

Simplify :$\frac{\sqrt[3]{8}}{\sqrt{16}}÷\frac{\sqrt{100}}{\sqrt{49}}\times \sqrt[3]{125}$

Answer 1

Simplify the expression:

$\begin{array}{l}\frac{\sqrt[3]{8}}{\sqrt{16}}÷\frac{\sqrt{100}}{\sqrt{49}}\times \sqrt[3]{125}\\ =\frac{\sqrt[3]{2^3}}{\sqrt{4^2}}+\frac{\sqrt{{10}^2}}{\sqrt{7^2}}\times \sqrt[3]{5^3}\\ =\frac{{\left(2^3\right)}^{{\displaystyle \frac{1}{3}}}}{{\left(4^2\right)}^{\frac{1}{2}}}+\frac{{\left({10}^2\right)}^{{\displaystyle \frac{1}{2}}}}{{\left(7^2\right)}^{\frac{1}{2}}}\times {\left(5^3\right)}^{\frac{1}{3}}\left[\because {\left(a^m\right)}^n=a^{m\times n}\right]\\ =\frac{2}{4}÷\frac{10}{7}\times 5\\ =\frac{2}{4}\times \frac{7}{10}\times 5\\ =\frac{7}{4}\\ =1\frac{3}{4}\end{array}$

The value of the given expression is $\frac{\sqrt[3]{8}}{\sqrt{16}}÷\frac{\sqrt{100}}{\sqrt{49}}\times \sqrt[3]{125}=1\frac{3}{4}$