Question

What is the following product?

Answer 1

`10√(3)`

Explanation:

One is given the following expression:

`√(30)*√(10)`

One property of multiplying square roots is that one can multiply the numbers under the radical by each other, and then put the radical on top of the result. The following is an example of this general format of this property:

`√(a)*√(b)=√(ab)`

Apply this to the real problem:

`√(30)*√(10)=√(30*10)`

Simplify,

`√(30*10)=√(300)`

Rewrite as (300) as the product of two numbers, such that one number is a perfect square:

`√(300)=√(3*10^2)`

Simplify, take a term out of the radical:

`√(3*10^2)=10√(3)`