Question

Which choice is equivalent to the quotient shown here when x > 0?

√72x^3 divide by square root of 50x^2

Answer 1

`(3√(2x))/(5)`

Explanation:

Starting point:

`(√(72x^3))/(50x^2)\\`

1) Factor it by Prime Factor Method 72 and 50

`72|2\\ 36|2\\ 18|2\\ 9|3\\3|3\\ 1\\ 72=2^2*3^2*2`

`50|2\\ 25|5\\ 5|5\\ 1\\ 50=2*5^2`

2) Plug it in the factored form. Every exponent to the second power will be outside the radical, so its roots.

`(√(72x^2*x))/(50x^2)=(6x√(2x))/(5x√(2))=(6√(x))/(5√(2))`

3) Rationalize it multiplying by the radical, so that you can eliminate the square root on the denominator.

`(6√(x))/(5√(2))*(√(2))/(√(2))=(6√(2x))/(10)=(3√(2x))/(5)`