Solve sqrt{100/24}

$$\sqrt{ \frac{ 100 }{ 24 } }$$

Evaluate

$$\frac{5\sqrt{6}}{6}\approx 2.041241452$$

Solution Steps

Reduce the fraction \frac{100}{24} to lowest terms by extracting and canceling out 4.

$$\sqrt{\frac{25}{6}}$$

Rewrite the square root of the division \sqrt{\frac{25}{6}} as the division of square roots \frac{\sqrt{25}}{\sqrt{6}}.

$$\frac{\sqrt{25}}{\sqrt{6}}$$

Calculate the square root of 25 and get 5.

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

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

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

The square of \sqrt{6} is 6.

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