Solve 4divsqrt{24}

$$4 \div \sqrt { 24 }$$

Evaluate

$$\frac{\sqrt{6}}{3}\approx 0.816496581$$

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}.

$$\frac{4}{2\sqrt{6}}$$

Rationalize the denominator of \frac{4}{2\sqrt{6}} by multiplying numerator and denominator by \sqrt{6}.

$$\frac{4\sqrt{6}}{2\left(\sqrt{6}\right)^{2}}$$

The square of \sqrt{6} is 6.

$$\frac{4\sqrt{6}}{2\times 6}$$

Cancel out 2\times 2 in both numerator and denominator.

$$\frac{\sqrt{6}}{3}$$