Solve sqrt{112}+sqrt{175}+sqrt{28}

$$\sqrt{ 112 } + \sqrt{ 175 } + \sqrt{ 28 }$$

Evaluate

$$11\sqrt{7}\approx 29.103264422$$

Solution Steps

Factor 112=4^{2}\times 7. Rewrite the square root of the product \sqrt{4^{2}\times 7} as the product of square roots \sqrt{4^{2}}\sqrt{7}. Take the square root of 4^{2}.

$$4\sqrt{7}+\sqrt{175}+\sqrt{28}$$

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}.

$$4\sqrt{7}+5\sqrt{7}+\sqrt{28}$$

Combine 4\sqrt{7} and 5\sqrt{7} to get 9\sqrt{7}.

$$9\sqrt{7}+\sqrt{28}$$

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}.

$$9\sqrt{7}+2\sqrt{7}$$

Combine 9\sqrt{7} and 2\sqrt{7} to get 11\sqrt{7}.

$$11\sqrt{7}$$