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

guringpw

guringpw

Answered question

2021-12-19

How do you simplify 45x3 ?

Answer & Explanation

eskalopit

eskalopit

Beginner2021-12-20Added 31 answers

=35x3
Explanation:
45x3
=45=335
So,
45x3=335x3
=35x3
Navreaiw

Navreaiw

Beginner2021-12-21Added 34 answers

Rewrite 45x3
Factor 9 out of 45.
9(5)x3
Rewrite 9 as 32
325x3
Factor out x2.
325(x2x)
Move 5.
32x25x
Rewrite 32x2 as (3x)2
(3x)25x
Add parentheses
(3x)2(5x)
Pull terms out from under the radical
3x5x
RizerMix

RizerMix

Expert2021-12-29Added 656 answers

Factor 45 into its prime factors
45=325
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=32
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:
35x3

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