# How do you simplify 4sqrt(50x^5)?

Sep 25, 2015

20${x}^{2} \sqrt{2 x}$

#### Explanation:

Prime factors of 50 are 2 * 5 * 5
And ${x}^{5}$ = ${x}^{2} \cdot {x}^{2} \cdot x$

Hence: $4 \sqrt{50 {x}^{5}}$ = $4 \sqrt{2 \cdot 5 \cdot 5 \cdot {x}^{2} \cdot {x}^{2} \cdot x}$
Since $\sqrt{5 \cdot 5}$ = 5 and $\sqrt{{x}^{2} \cdot {x}^{2}}$ = ${x}^{2}$

$4 \sqrt{50 {x}^{5}}$ = $4 \cdot 5 \cdot {x}^{2} \sqrt{2 \cdot x}$

= $20 {x}^{2} \sqrt{2 x}$