√(99) + √(44) in the form A√(B)

Question

`√(99) + √(44)` in the form A
`√(B)`

Answer 1

answer 5sqrt(11)

Explanation:

99 = 3 * 3 * 11

44 = 2 * 2 * 11

For every pair of equal prime factors under a square root sign, one can be take out and the other discarded.

sqrt(99) + sqrt(44)

sqrt(3 * 3 * 11) + sqrt(2 * 2 * 11)

Take a 3 out of sqrt (99) and a 2 out of square root(44)

3sqrt(11) + 2sqrt(11)

5 sqrt(11)