Solve [-7sqrt{3/7}]^2

$$[ - 7 \sqrt { \frac { 3 } { 7 } } ] ^ { 2 }$$

Evaluate

$$21$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{3}{7}} as the division of square roots \frac{\sqrt{3}}{\sqrt{7}}.

$$\left(-7\times \frac{\sqrt{3}}{\sqrt{7}}\right)^{2}$$

Rationalize the denominator of \frac{\sqrt{3}}{\sqrt{7}} by multiplying numerator and denominator by \sqrt{7}.

$$\left(-7\times \frac{\sqrt{3}\sqrt{7}}{\left(\sqrt{7}\right)^{2}}\right)^{2}$$

The square of \sqrt{7} is 7.

$$\left(-7\times \frac{\sqrt{3}\sqrt{7}}{7}\right)^{2}$$

To multiply \sqrt{3} and \sqrt{7}, multiply the numbers under the square root.

$$\left(-7\times \frac{\sqrt{21}}{7}\right)^{2}$$

Cancel out 7 and 7.

$$\left(-\sqrt{21}\right)^{2}$$

Expand \left(-\sqrt{21}\right)^{2}.

$$\left(-1\right)^{2}\left(\sqrt{21}\right)^{2}$$

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

$$1\left(\sqrt{21}\right)^{2}$$

The square of \sqrt{21} is 21.

$$1\times 21$$

Multiply 1 and 21 to get 21.

$$21$$

Factor

$$3\times 7$$