Evaluate
\frac{5\sqrt{70}}{14}\approx 2.988071523
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\frac{\sqrt{125}}{\sqrt{14}}
Rewrite the square root of the division \sqrt{\frac{125}{14}} as the division of square roots \frac{\sqrt{125}}{\sqrt{14}}.
\frac{5\sqrt{5}}{\sqrt{14}}
Factor 125=5^{2}\times 5. Rewrite the square root of the product \sqrt{5^{2}\times 5} as the product of square roots \sqrt{5^{2}}\sqrt{5}. Take the square root of 5^{2}.
\frac{5\sqrt{5}\sqrt{14}}{\left(\sqrt{14}\right)^{2}}
Rationalize the denominator of \frac{5\sqrt{5}}{\sqrt{14}} by multiplying numerator and denominator by \sqrt{14}.
\frac{5\sqrt{5}\sqrt{14}}{14}
The square of \sqrt{14} is 14.
\frac{5\sqrt{70}}{14}
To multiply \sqrt{5} and \sqrt{14}, multiply the numbers under the square root.
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