How do you simplify sqrt15 times sqrt21?

3 Answers
Aug 25, 2016

3sqrt35

Explanation:

When multiplying 2 square roots they can be combined into one.
Write each number as the product of its prime factors.

sqrt15 xxsqrt 21 = sqrt(5xx3xx3xx7

=3sqrt35

Aug 25, 2016

3sqrt35

Explanation:

When simplifying roots of natural numbers is is often useful to first express the numbers as the product of prime numbers.

Consider: 15 = 3xx5 and 21 = 3xx7

Also: sqrt15 xx sqrt21 = sqrt(15xx21)

= sqrt( 3xx5xx 3xx7)

=3sqrt(5xx7) = 3sqrt35

Aug 25, 2016

Same thing but with a slight twist in approach

3sqrt(35)

Explanation:

Look for common factors. Notice that 3 will divide into both 15 and 21 with no remainder.

Write as:" "sqrt(3xx5)xxsqrt(3xx7)

You can split these in the following way:

sqrt(3)xxsqrt(5)xxsqrt(3)xxsqrt(7)

But (sqrt(3))^2=3 giving:

3(sqrt(5)xxsqrt(7))

But sqrt(5)xxsqrt(7) is the same thing as sqrt(5xx7) =sqrt(35)

3sqrt(35)