Solve sqrt{7/128}

$$\sqrt { \frac { 7 } { 128 } }$$

Evaluate

$$\frac{\sqrt{14}}{16}\approx 0.233853587$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{7}{128}} as the division of square roots \frac{\sqrt{7}}{\sqrt{128}}.

$$\frac{\sqrt{7}}{\sqrt{128}}$$

Factor 128=8^{2}\times 2. Rewrite the square root of the product \sqrt{8^{2}\times 2} as the product of square roots \sqrt{8^{2}}\sqrt{2}. Take the square root of 8^{2}.

$$\frac{\sqrt{7}}{8\sqrt{2}}$$

Rationalize the denominator of \frac{\sqrt{7}}{8\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{\sqrt{7}\sqrt{2}}{8\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{\sqrt{7}\sqrt{2}}{8\times 2}$$

To multiply \sqrt{7} and \sqrt{2}, multiply the numbers under the square root.

$$\frac{\sqrt{14}}{8\times 2}$$

Multiply 8 and 2 to get 16.

$$\frac{\sqrt{14}}{16}$$