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

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Answer 1 · 2017-10-02T20:12:18

Answer: #20sqrt2 + 20sqrt15#

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.