Solve 1/sqrt{24}

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

Evaluate

$$\frac{\sqrt{6}}{12}\approx 0.204124145$$

Solution Steps

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}.

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

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

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

The square of \sqrt{6} is 6.

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

Multiply 2 and 6 to get 12.

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