Solve sqrt{500-16/5}

$$\sqrt{ 500- \frac{ 16 }{ 5 } }$$

Evaluate

$$\frac{6\sqrt{345}}{5}\approx 22.289010745$$

Solution Steps

Convert 500 to fraction \frac{2500}{5}.

$$\sqrt{\frac{2500}{5}-\frac{16}{5}}$$

Since \frac{2500}{5} and \frac{16}{5} have the same denominator, subtract them by subtracting their numerators.

$$\sqrt{\frac{2500-16}{5}}$$

Subtract 16 from 2500 to get 2484.

$$\sqrt{\frac{2484}{5}}$$

Rewrite the square root of the division \sqrt{\frac{2484}{5}} as the division of square roots \frac{\sqrt{2484}}{\sqrt{5}}.

$$\frac{\sqrt{2484}}{\sqrt{5}}$$

Factor 2484=6^{2}\times 69. Rewrite the square root of the product \sqrt{6^{2}\times 69} as the product of square roots \sqrt{6^{2}}\sqrt{69}. Take the square root of 6^{2}.

$$\frac{6\sqrt{69}}{\sqrt{5}}$$

Rationalize the denominator of \frac{6\sqrt{69}}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{6\sqrt{69}\sqrt{5}}{\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$\frac{6\sqrt{69}\sqrt{5}}{5}$$

To multiply \sqrt{69} and \sqrt{5}, multiply the numbers under the square root.

$$\frac{6\sqrt{345}}{5}$$