Solve 5sqrt{44}+2sqrt{94}-sqrt{176}

$$5 \sqrt { 44 } + 2 \sqrt { 94 } - \sqrt { 176 }$$

Evaluate

$$2\left(\sqrt{94}+3\sqrt{11}\right)\approx 39.290468172$$

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}.

$$5\times 2\sqrt{11}+2\sqrt{94}-\sqrt{176}$$

Multiply 5 and 2 to get 10.

$$10\sqrt{11}+2\sqrt{94}-\sqrt{176}$$

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}.

$$10\sqrt{11}+2\sqrt{94}-4\sqrt{11}$$

Combine 10\sqrt{11} and -4\sqrt{11} to get 6\sqrt{11}.

$$6\sqrt{11}+2\sqrt{94}$$