How do you evaluate 4\sqrt { 5} ( \sqrt { 10} + 5\sqrt { 3} )?

1 Answer
Oct 2, 2017

Answer: 20sqrt2 + 20sqrt15

Explanation:

First multiply out the brackets:

4sqrt5 (sqrt10 +5sqrt3 ) -> 4sqrt50 + 20sqrt15

Next simplify 4sqrt50:

sqrt50 = sqrt25 * sqrt2

sqrt25 = 5 as it is a square number.

Therefore:

4sqrt50 = 4*5*sqrt2 -> 20sqrt2

Answer: 20sqrt2 + 20sqrt15

Cannot be further evaluated due to the surds being different.