Solve sqrt{36-24/5}

$$\sqrt { 36 - \frac { 24 } { 5 } }$$

Evaluate

$$\frac{2\sqrt{195}}{5}\approx 5.585696018$$

Solution Steps

Convert 36 to fraction \frac{180}{5}.

$$\sqrt{\frac{180}{5}-\frac{24}{5}}$$

Since \frac{180}{5} and \frac{24}{5} have the same denominator, subtract them by subtracting their numerators.

$$\sqrt{\frac{180-24}{5}}$$

Subtract 24 from 180 to get 156.

$$\sqrt{\frac{156}{5}}$$

Rewrite the square root of the division \sqrt{\frac{156}{5}} as the division of square roots \frac{\sqrt{156}}{\sqrt{5}}.

$$\frac{\sqrt{156}}{\sqrt{5}}$$

Factor 156=2^{2}\times 39. Rewrite the square root of the product \sqrt{2^{2}\times 39} as the product of square roots \sqrt{2^{2}}\sqrt{39}. Take the square root of 2^{2}.

$$\frac{2\sqrt{39}}{\sqrt{5}}$$

Rationalize the denominator of \frac{2\sqrt{39}}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{2\sqrt{39}\sqrt{5}}{\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$\frac{2\sqrt{39}\sqrt{5}}{5}$$

To multiply \sqrt{39} and \sqrt{5}, multiply the numbers under the square root.

$$\frac{2\sqrt{195}}{5}$$