Solve sqrt{112}+sqrt{28}-sqrt{63}

$$\sqrt { 112 } + \sqrt { 28 } - \sqrt { 63 }$$

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}.

$$4\sqrt{7}+\sqrt{28}-\sqrt{63}$$

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}.

$$4\sqrt{7}+2\sqrt{7}-\sqrt{63}$$

Combine 4\sqrt{7} and 2\sqrt{7} to get 6\sqrt{7}.

$$6\sqrt{7}-\sqrt{63}$$

Factor 63=3^{2}\times 7. Rewrite the square root of the product \sqrt{3^{2}\times 7} as the product of square roots \sqrt{3^{2}}\sqrt{7}. Take the square root of 3^{2}.

$$6\sqrt{7}-3\sqrt{7}$$

Combine 6\sqrt{7} and -3\sqrt{7} to get 3\sqrt{7}.

$$3\sqrt{7}$$