How do you divide#sqrt125/sqrt5#?

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Answer 1 · 2015-03-22T17:35:33

Three methods:

The hard way

Rationalize the denominator.

#sqrt125/sqrt5=sqrt125/sqrt5*sqrt5/sqrt5=sqrt(125*5)/sqrt(5*5)=sqrt625/sqrt25=25/5=5#.

Two easy ways
First:
Simplify the numerator, then reduce the fraction.

#sqrt125/sqrt5=sqrt(25*5)/sqrt5=(5sqrt5)/sqrt5=5#.

Second:
Write as a single square root and reduce the fraction, then simplify:

#sqrt125/sqrt5=sqrt(125/5)=sqrt25=5#.