Solve sqrt{1000/24}

$$\sqrt{ \frac{ 1000 }{ 24 } }$$

Evaluate

$$\frac{5\sqrt{15}}{3}\approx 6.454972244$$

Solution Steps

Reduce the fraction \frac{1000}{24} to lowest terms by extracting and canceling out 8.

$$\sqrt{\frac{125}{3}}$$

Rewrite the square root of the division \sqrt{\frac{125}{3}} as the division of square roots \frac{\sqrt{125}}{\sqrt{3}}.

$$\frac{\sqrt{125}}{\sqrt{3}}$$

Factor 125=5^{2}\times 5. Rewrite the square root of the product \sqrt{5^{2}\times 5} as the product of square roots \sqrt{5^{2}}\sqrt{5}. Take the square root of 5^{2}.

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

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

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

The square of \sqrt{3} is 3.

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

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

$$\frac{5\sqrt{15}}{3}$$