Solve 5sqrt{99}-2sqrt{44}

$$5 \sqrt{ 99 } -2 \sqrt{ 44 }$$

Evaluate

$$11\sqrt{11}\approx 36.482872694$$

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}.

$$5\times 3\sqrt{11}-2\sqrt{44}$$

Multiply 5 and 3 to get 15.

$$15\sqrt{11}-2\sqrt{44}$$

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}.

$$15\sqrt{11}-2\times 2\sqrt{11}$$

Multiply -2 and 2 to get -4.

$$15\sqrt{11}-4\sqrt{11}$$

Combine 15\sqrt{11} and -4\sqrt{11} to get 11\sqrt{11}.

$$11\sqrt{11}$$