Solve left(sqrt{99}-sqrt{44}right)sqrt{11}

$$\left( \sqrt{ 99 } - \sqrt{ 44 } \right) \sqrt{ 11 }$$

Evaluate

$$11$$

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}.

$$\left(3\sqrt{11}-\sqrt{44}\right)\sqrt{11}$$

Factor 44=2^{2}\times 11. Rewrite the square root of the product \sqrt{2^{2}\times 11} as the product of square roots \sqrt{2^{2}}\sqrt{11}. Take the square root of 2^{2}.

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

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

$$\sqrt{11}\sqrt{11}$$

Multiply \sqrt{11} and \sqrt{11} to get 11.

$$11$$

Factor

$$11$$