Solve frac{(-11sqrt{7})^2}{77}-frac{sqrt{512}}{sqrt{8}}

$$\frac { ( - 11 \sqrt { 7 } ) ^ { 2 } } { 77 } - \frac { \sqrt { 512 } } { \sqrt { 8 } }$$

Evaluate

$$3$$

Solution Steps

Expand \left(-11\sqrt{7}\right)^{2}.

$$\frac{\left(-11\right)^{2}\left(\sqrt{7}\right)^{2}}{77}-\frac{\sqrt{512}}{\sqrt{8}}$$

Calculate -11 to the power of 2 and get 121.

$$\frac{121\left(\sqrt{7}\right)^{2}}{77}-\frac{\sqrt{512}}{\sqrt{8}}$$

The square of \sqrt{7} is 7.

$$\frac{121\times 7}{77}-\frac{\sqrt{512}}{\sqrt{8}}$$

Multiply 121 and 7 to get 847.

$$\frac{847}{77}-\frac{\sqrt{512}}{\sqrt{8}}$$

Divide 847 by 77 to get 11.

$$11-\frac{\sqrt{512}}{\sqrt{8}}$$

Rewrite the division of square roots \frac{\sqrt{512}}{\sqrt{8}} as the square root of the division \sqrt{\frac{512}{8}} and perform the division.

$$11-\sqrt{64}$$

Calculate the square root of 64 and get 8.

$$11-8$$

Subtract 8 from 11 to get 3.

$$3$$

Factor

$$3$$