Solve (2sqrt{28})^2=

$$( 2 \sqrt { 28 } ) ^ { 2 } =$$

Evaluate

$$112$$

Solution Steps

Factor 28=2^{2}\times 7. Rewrite the square root of the product \sqrt{2^{2}\times 7} as the product of square roots \sqrt{2^{2}}\sqrt{7}. Take the square root of 2^{2}.

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

Multiply 2 and 2 to get 4.

$$\left(4\sqrt{7}\right)^{2}$$

Expand \left(4\sqrt{7}\right)^{2}.

$$4^{2}\left(\sqrt{7}\right)^{2}$$

Calculate 4 to the power of 2 and get 16.

$$16\left(\sqrt{7}\right)^{2}$$

The square of \sqrt{7} is 7.

$$16\times 7$$

Multiply 16 and 7 to get 112.

$$112$$

Factor

$$2^{4}\times 7$$