Solve (-7sqrt{2/7})^2

$$( - 7 \sqrt { \frac { 2 } { 7 } } ) ^ { 2 }$$

Evaluate

$$14$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{2}{7}} as the division of square roots \frac{\sqrt{2}}{\sqrt{7}}.

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

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

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

The square of \sqrt{7} is 7.

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

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

$$\left(-7\times \frac{\sqrt{14}}{7}\right)^{2}$$

Cancel out 7 and 7.

$$\left(-\sqrt{14}\right)^{2}$$

Expand \left(-\sqrt{14}\right)^{2}.

$$\left(-1\right)^{2}\left(\sqrt{14}\right)^{2}$$

Calculate -1 to the power of 2 and get 1.

$$1\left(\sqrt{14}\right)^{2}$$

The square of \sqrt{14} is 14.

$$1\times 14$$

Multiply 1 and 14 to get 14.

$$14$$

Factor

$$2\times 7$$