Question

Which of the following is equivalent to 3sqrt ab/ 3sqrt 25?

Answer 1

Given

`\frac{\sqrt[3]{ab}}{\sqrt[3]{25}}`

Notice that,

`\frac{1}{\sqrt[3]{25}}=\frac{1}{25^{(1)/(3)}}=\frac{1}{5^{(2)/(3)}}=\frac{1}{5^{1-(1)/(3)}}=\frac{1}{5*5^{-(1)/(3)}}=(1)/(5)*5^{(1)/(3)}=\frac{\sqrt[3]{5}}{5}`

Therefore,

`\Rightarrow\frac{\sqrt[3]{ab}}{\sqrt[3]{25}}=\frac{\sqrt[3]{ab}*\sqrt[3]{5}}{5}=\frac{\sqrt[3]{5ab}}{5}`

Thus, the answer is (5ab)^(1/3)/5, the first option.