How do you divide $\frac{\sqrt{125}}{\sqrt{5}}$ $sqrt125/sqrt5$ ?

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How do you divide $\frac{\sqrt{125}}{\sqrt{5}}$ $sqrt125/sqrt5$ ?

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Answer 1 · 2015-03-22T17:35:33

Three methods:

The hard way

Rationalize the denominator.

$\frac{\sqrt{125}}{\sqrt{5}} = \frac{\sqrt{125}}{\sqrt{5}} \cdot \frac{\sqrt{5}}{\sqrt{5}} = \frac{\sqrt{125 \cdot 5}}{\sqrt{5 \cdot 5}} = \frac{\sqrt{625}}{\sqrt{25}} = \frac{25}{5} = 5$ $sqrt125/sqrt5=sqrt125/sqrt5*sqrt5/sqrt5=sqrt(125*5)/sqrt(5*5)=sqrt625/sqrt25=25/5=5$ .

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

$\frac{\sqrt{125}}{\sqrt{5}} = \frac{\sqrt{25 \cdot 5}}{\sqrt{5}} = \frac{5 \sqrt{5}}{\sqrt{5}} = 5$ $sqrt125/sqrt5=sqrt(25*5)/sqrt5=(5sqrt5)/sqrt5=5$ .

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

$\frac{\sqrt{125}}{\sqrt{5}} = \sqrt{\frac{125}{5}} = \sqrt{25} = 5$ $sqrt125/sqrt5=sqrt(125/5)=sqrt25=5$ .

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How do you divide $\frac{\sqrt{125}}{\sqrt{5}}$ $sqrt125/sqrt5$ ?

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How do you divide $\frac{\sqrt{125}}{\sqrt{5}}$ $sqrt125/sqrt5$ ?