Solve sqrt{15}divsqrt{50}

$$\sqrt{ 15 } \div \sqrt{ 50 }$$

Evaluate

$$\frac{\sqrt{30}}{10}\approx 0.547722558$$

Solution Steps

Factor 50=5^{2}\times 2. Rewrite the square root of the product \sqrt{5^{2}\times 2} as the product of square roots \sqrt{5^{2}}\sqrt{2}. Take the square root of 5^{2}.

$$\frac{\sqrt{15}}{5\sqrt{2}}$$

Rationalize the denominator of \frac{\sqrt{15}}{5\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{\sqrt{15}\sqrt{2}}{5\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{\sqrt{15}\sqrt{2}}{5\times 2}$$

To multiply \sqrt{15} and \sqrt{2}, multiply the numbers under the square root.

$$\frac{\sqrt{30}}{5\times 2}$$

Multiply 5 and 2 to get 10.

$$\frac{\sqrt{30}}{10}$$