How do you simplify 3w ^ { 2} \sqrt { 72w } - \sqrt { 50w ^ { 5} }?

2 Answers
Nov 15, 2017

=> 13 w^2 sqrt(2w)

Explanation:

3w ^ { 2} \sqrt { 72w } - \sqrt { 50w ^ { 5} }

=> 3w ^ { 2} \sqrt { 9xx4xx2xxw } - \sqrt { 25xx2xxw ^ { 5} }

=> 3w ^ { 2} xx3xx2\sqrt { 2w } - 5\sqrt { 2wxxw ^ { 4} }

=> 18w ^ { 2}\sqrt { 2w } - 5w^2\sqrt { 2w}

=> (18- 5)w ^ { 2}\sqrt { 2w }

=> 13 w^2 sqrt(2w)

Nov 15, 2017

13w^2sqrt(2w)

Explanation:

Pull the perfect squares out of the square roots

3w^2sqrt(72w)-sqrt(50w^5)

=3w^2sqrt(36*2w)-sqrt(25*2w^5)

=3w^2sqrt(36)sqrt(2w)-sqrt(25)sqrt(2w^5)

=3w^2*6sqrt(2w)-5sqrt(2w^5)

Next, you can simplify the w^5 by rewriting it as w^(4+1)=w^4w^1.

=18w^2sqrt(2w)-5sqrt(2w^4w^1)

=18w^2sqrt(2w)-5w^2sqrt(2w)

The sqrt(2w) factors out of both terms

=(18w^2-5w^2)sqrt(2w)

The terms on the left simplify

=13w^2sqrt(2w)