Solve 5sqrt{1/24}

$$5 \sqrt { \frac { 1 } { 24 } }$$

Evaluate

$$\frac{5\sqrt{6}}{12}\approx 1.020620726$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{1}{24}} as the division of square roots \frac{\sqrt{1}}{\sqrt{24}}.

$$5\times \frac{\sqrt{1}}{\sqrt{24}}$$

Calculate the square root of 1 and get 1.

$$5\times \frac{1}{\sqrt{24}}$$

Factor 24=2^{2}\times 6. Rewrite the square root of the product \sqrt{2^{2}\times 6} as the product of square roots \sqrt{2^{2}}\sqrt{6}. Take the square root of 2^{2}.

$$5\times \frac{1}{2\sqrt{6}}$$

Rationalize the denominator of \frac{1}{2\sqrt{6}} by multiplying numerator and denominator by \sqrt{6}.

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

The square of \sqrt{6} is 6.

$$5\times \frac{\sqrt{6}}{2\times 6}$$

Multiply 2 and 6 to get 12.

$$5\times \frac{\sqrt{6}}{12}$$

Express 5\times \frac{\sqrt{6}}{12} as a single fraction.

$$\frac{5\sqrt{6}}{12}$$