How do you simplify 10 square root 6 times square root 2?

1 Answer
Sep 8, 2015

By using
sqrt(a) xx sqrt(b) = sqrt(ab),

10sqrt(6) xx sqrt(2) = 20sqrt(3)

Explanation:

To simplify 10sqrt(6) xx sqrt(2) we just need to keep in mind the following rule regarding radicals:

sqrt(a) xx sqrt(b) = sqrt(ab)

This means that:

10sqrt(6) xx sqrt(2)
= 10sqrt(6*2
10sqrt(12)

From this step, we need to check if we can factor out any perfect squares from 12. If there is a perfect square, we can factor it out to simplify it more.

4 is a perfect square, and we can factor out 4 from 12 since 12 = 4 xx 3. We just apply the rule in reverse, splitting the radical.

10sqrt(12)
=10sqrt(4 xx 3)
=10sqrt(4)xxsqrt(3)
=10xx2xxsqrt(3)
=20sqrt(3)