 guringpw

2021-12-19

How do you simplify $\sqrt{45{x}^{3}}$ ? eskalopit

Expert

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

Expert

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

Expert

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:
$3\cdot \sqrt{5{x}^{3}}$

Do you have a similar question?