Question

simplify$( \sqrt{5} )( \sqrt[3]{5} )$a. 5 5/6b. 5 1/6c. 5 2/3d. 5 7/6

Answer 1

To solve the exercise you can use the following properties of radicals and exponents

$\sqrt[n]{a^m}=a^{\frac{m}{n}}$$a^ma^n=a^{m+n}$

So, in this case, you have

$\sqrt[]{5\text{ }}=5^{\frac{1}{2}}$$\sqrt[3]{5}=5^{\frac{1}{3}}$

And finally,

$\sqrt[]{5}\sqrt[3]{5}=5^{\frac{1}{2}}5^{\frac{1}{3}}=5^{\frac{1}{2}+\frac{1}{3}}=5^{\frac{3+2}{6}}=5^{\frac{5}{6}}$

Therefore, the correct answer is A.

$5^{\frac{5}{6}}$