Solve frac{sqrt{15}}{sqrt{10}}=

$$\frac{ \sqrt{ 15 } }{ \sqrt{ 10 } } =$$

Evaluate

$$\frac{\sqrt{6}}{2}\approx 1.224744871$$

Solution Steps

Rationalize the denominator of \frac{\sqrt{15}}{\sqrt{10}} by multiplying numerator and denominator by \sqrt{10}.

$$\frac{\sqrt{15}\sqrt{10}}{\left(\sqrt{10}\right)^{2}}$$

The square of \sqrt{10} is 10.

$$\frac{\sqrt{15}\sqrt{10}}{10}$$

To multiply \sqrt{15} and \sqrt{10}, multiply the numbers under the square root.

$$\frac{\sqrt{150}}{10}$$

Factor 150=5^{2}\times 6. Rewrite the square root of the product \sqrt{5^{2}\times 6} as the product of square roots \sqrt{5^{2}}\sqrt{6}. Take the square root of 5^{2}.

$$\frac{5\sqrt{6}}{10}$$

Divide 5\sqrt{6} by 10 to get \frac{1}{2}\sqrt{6}.

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