Solve 9sqrt{11}-3sqrt{44}+sqrt{99}

$$9 \sqrt { 11 } - 3 \sqrt { 44 } + \sqrt { 99 }$$

Evaluate

$$6\sqrt{11}\approx 19.899748742$$

Solution Steps

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}.

$$9\sqrt{11}-3\times 2\sqrt{11}+\sqrt{99}$$

Multiply -3 and 2 to get -6.

$$9\sqrt{11}-6\sqrt{11}+\sqrt{99}$$

Combine 9\sqrt{11} and -6\sqrt{11} to get 3\sqrt{11}.

$$3\sqrt{11}+\sqrt{99}$$

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}.

$$3\sqrt{11}+3\sqrt{11}$$

Combine 3\sqrt{11} and 3\sqrt{11} to get 6\sqrt{11}.

$$6\sqrt{11}$$