Solve sqrt{(-2)^2}+(-2sqrt{3})^2-sqrt{7}(3sqrt{28}-frac{sqrt{4}}{sqrt{7}})

$$\sqrt { ( - 2 ) ^ { 2 } } + ( - 2 \sqrt { 3 } ) ^ { 2 } - \sqrt { 7 } ( 3 \sqrt { 28 } - \frac { \sqrt { 4 } } { \sqrt { 7 } } )$$

Evaluate

$$-26$$

Solution Steps

Calculate -2 to the power of 2 and get 4.

$$\sqrt{4}+\left(-2\sqrt{3}\right)^{2}-\sqrt{7}\left(3\sqrt{28}-\frac{\sqrt{4}}{\sqrt{7}}\right)$$

Calculate the square root of 4 and get 2.

$$2+\left(-2\sqrt{3}\right)^{2}-\sqrt{7}\left(3\sqrt{28}-\frac{\sqrt{4}}{\sqrt{7}}\right)$$

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

$$2+\left(-2\right)^{2}\left(\sqrt{3}\right)^{2}-\sqrt{7}\left(3\sqrt{28}-\frac{\sqrt{4}}{\sqrt{7}}\right)$$

Calculate -2 to the power of 2 and get 4.

$$2+4\left(\sqrt{3}\right)^{2}-\sqrt{7}\left(3\sqrt{28}-\frac{\sqrt{4}}{\sqrt{7}}\right)$$

The square of \sqrt{3} is 3.

$$2+4\times 3-\sqrt{7}\left(3\sqrt{28}-\frac{\sqrt{4}}{\sqrt{7}}\right)$$

Multiply 4 and 3 to get 12.

$$2+12-\sqrt{7}\left(3\sqrt{28}-\frac{\sqrt{4}}{\sqrt{7}}\right)$$

Add 2 and 12 to get 14.

$$14-\sqrt{7}\left(3\sqrt{28}-\frac{\sqrt{4}}{\sqrt{7}}\right)$$

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}.

$$14-\sqrt{7}\left(3\times 2\sqrt{7}-\frac{\sqrt{4}}{\sqrt{7}}\right)$$

Multiply 3 and 2 to get 6.

$$14-\sqrt{7}\left(6\sqrt{7}-\frac{\sqrt{4}}{\sqrt{7}}\right)$$

Calculate the square root of 4 and get 2.

$$14-\sqrt{7}\left(6\sqrt{7}-\frac{2}{\sqrt{7}}\right)$$

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

$$14-\sqrt{7}\left(6\sqrt{7}-\frac{2\sqrt{7}}{\left(\sqrt{7}\right)^{2}}\right)$$

The square of \sqrt{7} is 7.

$$14-\sqrt{7}\left(6\sqrt{7}-\frac{2\sqrt{7}}{7}\right)$$

Combine 6\sqrt{7} and -\frac{2\sqrt{7}}{7} to get \frac{40}{7}\sqrt{7}.

$$14-\sqrt{7}\times \frac{40}{7}\sqrt{7}$$

Multiply \sqrt{7} and \sqrt{7} to get 7.

$$14-7\times \frac{40}{7}$$

Multiply 7 and \frac{40}{7} to get 40.

$$14-40$$

Subtract 40 from 14 to get -26.

$$-26$$

Factor

$$-26$$