Question

Simplify square root of 3 multiplied by the fifth root of 3.

Answer 1

3 7/10

Explanation:

ur mom told me last night

(also i got it correct on my quiz)

Answer 2

`\bf a^{\frac{{ n}}{{ m}}} \implies \sqrt[{ m}]{a^( n)} \qquad \qquad \sqrt[{ m}]{a^( n)}\implies a^{\frac{{ n}}{{ m}}} \\\quad \\% rational negative exponent a^{-\frac{{ n}}{{ m}}} = \cfrac{1}{a^{\frac{{ n}}{{ m}}}} \implies \cfrac{1}{\sqrt[{ m}]{a^( n)}}\qquad\qquad % radical denominator \cfrac{1}{\sqrt[{ m}]{a^( n)}}= \cfrac{1}{a^{\frac{{ n}}{{ m}}}}\implies a^{-\frac{{ n}}{{ m}}} \\\\`


`\bf -----------------------------\\\\ thus\qquad √(3)\cdot \sqrt[5]{3}\implies \sqrt[2]{3^1}\cdot \sqrt[5]{3^1}\implies 3^{(1)/(2)}\cdot 3^{(1)/(5)} \\\\\\ 3^{(1)/(2)+(1)/(5)}\implies 3^{(7)/(10)}\implies \sqrt[10]{3^7}\implies \sqrt[10]{2187}`