Solve frac{sqrt{15}}{sqrt{24}}

$$\frac { \sqrt { 15 } } { \sqrt { 24 } }$$

Evaluate

$$\frac{\sqrt{10}}{4}\approx 0.790569415$$

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}.

$$\frac{\sqrt{15}}{2\sqrt{6}}$$

Rationalize the denominator of \frac{\sqrt{15}}{2\sqrt{6}} by multiplying numerator and denominator by \sqrt{6}.

$$\frac{\sqrt{15}\sqrt{6}}{2\left(\sqrt{6}\right)^{2}}$$

The square of \sqrt{6} is 6.

$$\frac{\sqrt{15}\sqrt{6}}{2\times 6}$$

To multiply \sqrt{15} and \sqrt{6}, multiply the numbers under the square root.

$$\frac{\sqrt{90}}{2\times 6}$$

Multiply 2 and 6 to get 12.

$$\frac{\sqrt{90}}{12}$$

Factor 90=3^{2}\times 10. Rewrite the square root of the product \sqrt{3^{2}\times 10} as the product of square roots \sqrt{3^{2}}\sqrt{10}. Take the square root of 3^{2}.

$$\frac{3\sqrt{10}}{12}$$

Divide 3\sqrt{10} by 12 to get \frac{1}{4}\sqrt{10}.

$$\frac{1}{4}\sqrt{10}$$