How do you simplify 45x3 ?

${\displaystyle =3\sqrt{5x^3}}$
Explanation:
${\displaystyle \sqrt{45x^3}}$
${\displaystyle =\sqrt{45}=\sqrt{3\cdot 3\cdot 5}}$
So,
${\displaystyle \sqrt{45x^3}=\sqrt{3\cdot 3\cdot 5\cdot x^3}}$
${\displaystyle =3\sqrt{5x^3}}$

Rewrite ${\displaystyle 45x^3}$
Factor 9 out of 45.
${\displaystyle \sqrt{9\left(5\right)x^3}}$
Rewrite 9 as ${\displaystyle 3^2}$
${\displaystyle \sqrt{3^2\cdot 5x^3}}$
Factor out ${\displaystyle x^2}$.
${\displaystyle \sqrt{3^2\cdot 5\left(x^{2}x\right)}}$
Move 5.
${\displaystyle \sqrt{3^2{x}^2\cdot 5x}}$
Rewrite ${\displaystyle 3^2{x}^2}$ as ${\displaystyle {\left(3x\right)}^2}$
${\displaystyle \sqrt{{\left(3x\right)}^2\cdot 5x}}$
Add parentheses
${\displaystyle \sqrt{{\left(3x\right)}^2\cdot \left(5x\right)}}$
Pull terms out from under the radical
${\displaystyle 3x\sqrt{5x}}$

Factor 45 into its prime factors
$45=3^2\cdot 5$
To simplify a square root, we extract factors which are squares, i.e., factors that are raised to an even exponent.
Factors which will be extracted are:
$9=3^2$
Factors which will remain inside the root are:
$5=5$
To complete this part of the simplification we take the squre root of the factors which are to be extracted. We do this by dividing their exponents by 2 :
$3=3$
At the end of this step the partly simplified SQRT looks like this:
$3\cdot \sqrt{5x^3}$