How do you simplify 25/sqrt12525√125?

2 Answers
JS
May 30, 2017

5/(sqrt(5)5√5

Explanation:

25/sqrt(125)25√125

Let's rewrite the denominator.

25/((sqrt(25))(sqrt(5)))25(√25)(√5)

Simplify

25/(5(sqrt(5)))255(√5)

5/(sqrt(5)5√5

Rationalise the denominator

= frac(5)(sqrt(5)) cdot frac(sqrt(5))(sqrt(5))=5√5⋅√5√5

= frac(5 sqrt(5))(5)=5√55

= sqrt(5)=√5

Tazwar Sikder
May 30, 2017

sqrt(5)√5

Explanation:

We have: frac(25)(sqrt(125))25√125

Let's express the denominator as a product:

= frac(25)(sqrt(5^(2) cdot 5))=25√52⋅5

= frac(25)(5 sqrt(5))=255√5

= frac(5)(sqrt(5))=5√5

Then, let's rationalise the denominator:

= frac(5)(sqrt(5)) cdot frac(sqrt(5))(sqrt(5))=5√5⋅√5√5

= frac(5 sqrt(5))(5)=5√55

= sqrt(5)=√5

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