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

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Answer 1 · 2017-11-15T06:15:26

$=> 13 w^2 sqrt(2w)$

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

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

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

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

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

$=> 13 w^2 sqrt(2w)$

Answer 2 · 2017-11-15T06:20:46

$13w^2sqrt(2w)$

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

$=13w^2sqrt(2w)$

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