Solve sqrt{112}-sqrt{28}+sqrt{7}

$$\sqrt { 112 } - \sqrt { 28 } + \sqrt { 7 }$$

Evaluate

$$3\sqrt{7}\approx 7.937253933$$

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}.

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

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}.

$$4\sqrt{7}-2\sqrt{7}+\sqrt{7}$$

Combine 4\sqrt{7} and -2\sqrt{7} to get 2\sqrt{7}.

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

Combine 2\sqrt{7} and \sqrt{7} to get 3\sqrt{7}.

$$3\sqrt{7}$$