Solve 5sqrt{44}+2sqrt{99}-sqrt{176}

$$5 \sqrt{ 44 } +2 \sqrt{ 99 } - \sqrt{ 176 }$$

Evaluate

$$12\sqrt{11}\approx 39.799497484$$

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}.

$$5\times 2\sqrt{11}+2\sqrt{99}-\sqrt{176}$$

Multiply 5 and 2 to get 10.

$$10\sqrt{11}+2\sqrt{99}-\sqrt{176}$$

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}.

$$10\sqrt{11}+2\times 3\sqrt{11}-\sqrt{176}$$

Multiply 2 and 3 to get 6.

$$10\sqrt{11}+6\sqrt{11}-\sqrt{176}$$

Combine 10\sqrt{11} and 6\sqrt{11} to get 16\sqrt{11}.

$$16\sqrt{11}-\sqrt{176}$$

Factor 176=4^{2}\times 11. Rewrite the square root of the product \sqrt{4^{2}\times 11} as the product of square roots \sqrt{4^{2}}\sqrt{11}. Take the square root of 4^{2}.

$$16\sqrt{11}-4\sqrt{11}$$

Combine 16\sqrt{11} and -4\sqrt{11} to get 12\sqrt{11}.

$$12\sqrt{11}$$