Solve sqrt{64/76}

$$\sqrt { 6 \frac { 4 } { 76 } }$$

Evaluate

$$\frac{\sqrt{2185}}{19}\approx 2.460209662$$

Solution Steps

Multiply 6 and 76 to get 456.

$$\sqrt{\frac{456+4}{76}}$$

Add 456 and 4 to get 460.

$$\sqrt{\frac{460}{76}}$$

Reduce the fraction \frac{460}{76} to lowest terms by extracting and canceling out 4.

$$\sqrt{\frac{115}{19}}$$

Rewrite the square root of the division \sqrt{\frac{115}{19}} as the division of square roots \frac{\sqrt{115}}{\sqrt{19}}.

$$\frac{\sqrt{115}}{\sqrt{19}}$$

Rationalize the denominator of \frac{\sqrt{115}}{\sqrt{19}} by multiplying numerator and denominator by \sqrt{19}.

$$\frac{\sqrt{115}\sqrt{19}}{\left(\sqrt{19}\right)^{2}}$$

The square of \sqrt{19} is 19.

$$\frac{\sqrt{115}\sqrt{19}}{19}$$

To multiply \sqrt{115} and \sqrt{19}, multiply the numbers under the square root.

$$\frac{\sqrt{2185}}{19}$$