Solve (sqrt{99}-sqrt{11})^2

$$( \sqrt { 99 } - \sqrt { 11 } ) ^ { 2 }$$

Evaluate

$$44$$

Solution Steps

Factor 99=3^{2}\times 11. Rewrite the square root of the product \sqrt{3^{2}\times 11} as the product of square roots \sqrt{3^{2}}\sqrt{11}. Take the square root of 3^{2}.

$$\left(3\sqrt{11}-\sqrt{11}\right)^{2}$$

Combine 3\sqrt{11} and -\sqrt{11} to get 2\sqrt{11}.

$$\left(2\sqrt{11}\right)^{2}$$

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

$$2^{2}\left(\sqrt{11}\right)^{2}$$

Calculate 2 to the power of 2 and get 4.

$$4\left(\sqrt{11}\right)^{2}$$

The square of \sqrt{11} is 11.

$$4\times 11$$

Multiply 4 and 11 to get 44.

$$44$$

Factor

$$2^{2}\times 11$$