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

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

Evaluate

$$63$$

Solution Steps

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

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

The square of \sqrt{7} is 7.

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

Cancel out 7 and 7.

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

Combine \sqrt{7} and 2\sqrt{7} to get 3\sqrt{7}.

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

Expand \left(3\sqrt{7}\right)^{2}.

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

Calculate 3 to the power of 2 and get 9.

$$9\left(\sqrt{7}\right)^{2}$$

The square of \sqrt{7} is 7.

$$9\times 7$$

Multiply 9 and 7 to get 63.

$$63$$

Factor

$$3^{2}\times 7$$