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 am × an = am+n under exponent rule

Answer: Square root of 3 multiplied by the fifth root of 3 is 3(710)

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

Explanation:

As per the product law,

am × an = am+n 

Square root of 3 = 312

Fifth root of 3 = 315     

Here we have a = 3, m = 12 and n = 15

= 312 × 315

= 3(12+15)

= 3(5+210)

= 3(710)

Hence, the square root of 3 multiplied by the fifth root of 3 is 3(710)