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How do you simplify #sqrt(125a^3)#?

Answer 1

Eva Adamson

Factor it out.

Break down the expression into its factors:

#sqrt(125a^3)=sqrt(5*5*5*a*a*a)#

Notice that we have a pair of #5#'s and #a#'s.

#sqrt(5*5*5*a*a*a)=sqrt(5*(5*5)•a*(a*a)) =sqrt(5*(5)^2*a*(a^2))#

We can take these (the pairs) out of the expression.

#sqrt(5*(5)^2*a*(a^2)) =5*a*sqrt(5*a)#

Finally,

#5*a*sqrt(5*a)=5a sqrt(5a)#

#sqrt(125a^3)=5a sqrt(5a)#

Hope this helps!

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Answer 2

Hazel Anglin

To simplify ( \sqrt{125a^3} ), you can break down the expression as follows:

( \sqrt{125a^3} = \sqrt{25 \cdot 5 \cdot a^2 \cdot a} )

Using the property ( \sqrt{xy} = \sqrt{x} \cdot \sqrt{y} ), we can simplify further:

( \sqrt{25 \cdot 5 \cdot a^2 \cdot a} = \sqrt{25} \cdot \sqrt{5} \cdot \sqrt{a^2} \cdot \sqrt{a} )

( = 5 \cdot \sqrt{5} \cdot a \cdot \sqrt{a} )

Therefore, ( \sqrt{125a^3} ) simplifies to ( 5a\sqrt{5a} ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.