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

## Question: Simplify square root of 3 multiplied by the fifth root of 3.

Let's look into the product law a^{m} × a^{n} = a^{m+n} under exponent rule

## Answer: Square root of 3 multiplied by the fifth root of 3 is 3^{(7⁄10)}

Let's put the question in form of expression and solve further

## Explanation:

As per the product law,

a^{m} × a^{n} = a^{m+n}

Square root of 3 = 3^{1⁄2}

Fifth root of 3 = 3^{1⁄5}

Here we have a = 3, m = ^{1}⁄_{2} and n = ^{1}⁄_{5}

= 3^{1⁄2} × 3^{1⁄5}

= 3^{(1⁄2+1⁄5)}

= 3^{(5+2⁄10)}

= 3^{(7⁄10)}

### Hence, the square root of 3 multiplied by the fifth root of 3 is 3^{(7⁄10)}

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