Solve (sqrt{7}-sqrt{28})^2

$$( \sqrt { 7 } - \sqrt { 28 } ) ^ { 2 }$$

Evaluate

$$7$$

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}.

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

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

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

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

$$\left(-1\right)^{2}\left(\sqrt{7}\right)^{2}$$

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

$$1\left(\sqrt{7}\right)^{2}$$

The square of \sqrt{7} is 7.

$$1\times 7$$

Multiply 1 and 7 to get 7.

$$7$$

Factor

$$7$$