Question

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

Answer 1

20`x^2sqrt(2x)`

Explanation:

Prime factors of 50 are 2 * 5 * 5
And `x^5` = `x^2 * x^2 * x`

Hence: `4sqrt(50x^5)` = `4sqrt(2 * 5 * 5 * x^2 * x^2 * x)`
Since `sqrt(5*5)` = 5 and `sqrt(x^2 * x^2)` = `x^2`

`4sqrt(50x^5)` = `4*5*x^2sqrt(2*x)`

= `20x^2sqrt(2x)`