Question

How would you simplify `sqrt (9x^3)`?

Answer 1

`3xsqrt(x)`

Explanation:

We start out with `sqrt(9x^3)`. To solve this we simplify the values into their smallest factors. For `9`, that's pretty easy; the smallest it goes is `3*3` or `3^2`. `x^3` can be simplified to `x*x*x` or `x^2*x`.

If we rewrite the expression, it becomes `sqrt(3^2*x^2*x)`. Square root of a square cancels out, like this `cancel(sqrt(3^cancel(2)`.

`sqrt(3^2)` is just `3`. Likewise `sqrt(x^2)` simplifys to `x`. Now the expression is `3xsqrtx`.