Solve sqrt{624/25}div1/5

$$\sqrt{ \frac{ 624 }{ 25 } } \div \frac{ 1 }{ 5 }$$

Evaluate

$$4\sqrt{39}\approx 24.979991994$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{624}{25}} as the division of square roots \frac{\sqrt{624}}{\sqrt{25}}.

$$\frac{\frac{\sqrt{624}}{\sqrt{25}}}{\frac{1}{5}}$$

Factor 624=4^{2}\times 39. Rewrite the square root of the product \sqrt{4^{2}\times 39} as the product of square roots \sqrt{4^{2}}\sqrt{39}. Take the square root of 4^{2}.

$$\frac{\frac{4\sqrt{39}}{\sqrt{25}}}{\frac{1}{5}}$$

Calculate the square root of 25 and get 5.

$$\frac{\frac{4\sqrt{39}}{5}}{\frac{1}{5}}$$

Divide \frac{4\sqrt{39}}{5} by \frac{1}{5} by multiplying \frac{4\sqrt{39}}{5} by the reciprocal of \frac{1}{5}.

$$\frac{4\sqrt{39}\times 5}{5}$$

Cancel out 5 and 5.

$$4\sqrt{39}$$