Simplify square root of 3 times square root of 21.

Solution:

Given square root of 3 times square root of 21.

You know that for real, positive numbers you have

√a⋅√b = √a⋅b

This means that you can write

√3⋅√21 = √{3⋅21}

If you write 21 as the product of its prime factors 3 and 7, you can say that

√3⋅21 = √3⋅3⋅7 = √9⋅7

Now use the same multiplication property of radicals to write

√9⋅7 = √9⋅√7 = 3⋅√7 = 3√7

Simplify square root of 3 times square root of 21.

Summary:

Square root of 3 times square root of 21 simplified as 3√7.