How do you simplify 6sqrt18 + 3sqrt50?

1 Answer
Jun 6, 2016

33sqrt(2)

Explanation:

Consider 18 and 50 as products of primes:

18 = 2 times 9 = 2 times 3^2 and 50 = 2 times 25 = 2 times 5^2

This means that

sqrt(18) = sqrt(2 times 3^2) = sqrt(2)sqrt(3^2) = 3sqrt(2)

and similarly, sqrt(50) = 5sqrt(2).

Thus, 6sqrt(18) + 3sqrt(50) can be simplified as such:
6sqrt(18) + 3sqrt(50) = 6(3sqrt(2)) + 3(5sqrt(2)) = 18sqrt(2) + 15sqrt(2) = 33sqrt(2)