Solve sqrt{87/50}

$$\sqrt { \frac { 87 } { 50 } }$$

Evaluate

$$\frac{\sqrt{174}}{10}\approx 1.319090596$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{87}{50}} as the division of square roots \frac{\sqrt{87}}{\sqrt{50}}.

$$\frac{\sqrt{87}}{\sqrt{50}}$$

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}.

$$\frac{\sqrt{87}}{5\sqrt{2}}$$

Rationalize the denominator of \frac{\sqrt{87}}{5\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{\sqrt{87}\sqrt{2}}{5\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{\sqrt{87}\sqrt{2}}{5\times 2}$$

To multiply \sqrt{87} and \sqrt{2}, multiply the numbers under the square root.

$$\frac{\sqrt{174}}{5\times 2}$$

Multiply 5 and 2 to get 10.

$$\frac{\sqrt{174}}{10}$$