Solve sqrt{64-32+4/64-4}

$$\sqrt { \frac { 64 - 32 + 4 } { 64 - 4 } }$$

Evaluate

$$\frac{\sqrt{15}}{5}\approx 0.774596669$$

Solution Steps

Subtract 32 from 64 to get 32.

$$\sqrt{\frac{32+4}{64-4}}$$

Add 32 and 4 to get 36.

$$\sqrt{\frac{36}{64-4}}$$

Subtract 4 from 64 to get 60.

$$\sqrt{\frac{36}{60}}$$

Reduce the fraction \frac{36}{60} to lowest terms by extracting and canceling out 12.

$$\sqrt{\frac{3}{5}}$$

Rewrite the square root of the division \sqrt{\frac{3}{5}} as the division of square roots \frac{\sqrt{3}}{\sqrt{5}}.

$$\frac{\sqrt{3}}{\sqrt{5}}$$

Rationalize the denominator of \frac{\sqrt{3}}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{\sqrt{3}\sqrt{5}}{\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$\frac{\sqrt{3}\sqrt{5}}{5}$$

To multiply \sqrt{3} and \sqrt{5}, multiply the numbers under the square root.

$$\frac{\sqrt{15}}{5}$$