Solve sqrt{44}+sqrt{175}+sqrt{99}+sqrt{28}=

$$\sqrt { 44 } + \sqrt { 175 } + \sqrt { 99 } + \sqrt { 28 } =$$

Evaluate

$$5\sqrt{11}+7\sqrt{7}\approx 35.103383129$$

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}.

$$2\sqrt{11}+\sqrt{175}+\sqrt{99}+\sqrt{28}$$

Factor 175=5^{2}\times 7. Rewrite the square root of the product \sqrt{5^{2}\times 7} as the product of square roots \sqrt{5^{2}}\sqrt{7}. Take the square root of 5^{2}.

$$2\sqrt{11}+5\sqrt{7}+\sqrt{99}+\sqrt{28}$$

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}.

$$2\sqrt{11}+5\sqrt{7}+3\sqrt{11}+\sqrt{28}$$

Combine 2\sqrt{11} and 3\sqrt{11} to get 5\sqrt{11}.

$$5\sqrt{11}+5\sqrt{7}+\sqrt{28}$$

Factor 28=2^{2}\times 7. Rewrite the square root of the product \sqrt{2^{2}\times 7} as the product of square roots \sqrt{2^{2}}\sqrt{7}. Take the square root of 2^{2}.

$$5\sqrt{11}+5\sqrt{7}+2\sqrt{7}$$

Combine 5\sqrt{7} and 2\sqrt{7} to get 7\sqrt{7}.

$$5\sqrt{11}+7\sqrt{7}$$