Solve sqrt{209/32}

$$\sqrt { \frac { 209 } { 32 } }$$

Evaluate

$$\frac{\sqrt{418}}{8}\approx 2.555631038$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{209}{32}} as the division of square roots \frac{\sqrt{209}}{\sqrt{32}}.

$$\frac{\sqrt{209}}{\sqrt{32}}$$

Factor 32=4^{2}\times 2. Rewrite the square root of the product \sqrt{4^{2}\times 2} as the product of square roots \sqrt{4^{2}}\sqrt{2}. Take the square root of 4^{2}.

$$\frac{\sqrt{209}}{4\sqrt{2}}$$

Rationalize the denominator of \frac{\sqrt{209}}{4\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{\sqrt{209}\sqrt{2}}{4\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{\sqrt{209}\sqrt{2}}{4\times 2}$$

To multiply \sqrt{209} and \sqrt{2}, multiply the numbers under the square root.

$$\frac{\sqrt{418}}{4\times 2}$$

Multiply 4 and 2 to get 8.

$$\frac{\sqrt{418}}{8}$$