"How do you simplify 45x3 ?" was answered by students like you

High School
Algebra
Algebra I
Exponents and radicals

guringpw

Answered question

2021-12-19

How do you simplify

\sqrt{45 x^{3}}

Answer & Explanation

eskalopit

Beginner2021-12-20Added 31 answers

= 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

Beginner2021-12-21Added 34 answers

Rewrite

45 x^{3}

Factor 9 out of 45.

\sqrt{9 (5) x^{3}}

Rewrite 9 as

3^{2}

\sqrt{3^{2} \cdot 5 x^{3}}

Factor out

x^{2}

\sqrt{3^{2} \cdot 5 (x^{2} x)}

Move 5.

\sqrt{3^{2} x^{2} \cdot 5 x}

Rewrite

3^{2} x^{2}

{(3 x)}^{2}

\sqrt{{(3 x)}^{2} \cdot 5 x}

Add parentheses

\sqrt{{(3 x)}^{2} \cdot (5 x)}

Pull terms out from under the radical

3 x \sqrt{5 x}

RizerMix

Expert2021-12-29Added 656 answers

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

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