Solve sqrt{112}+sqrt{63}-2sqrt{232}

$$\sqrt { 112 } + \sqrt { 63 } - 2 \sqrt { 232 }$$

Evaluate

$$7\sqrt{7}-4\sqrt{58}\approx -11.942833246$$

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}.

$$4\sqrt{7}+\sqrt{63}-2\sqrt{232}$$

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}.

$$4\sqrt{7}+3\sqrt{7}-2\sqrt{232}$$

Combine 4\sqrt{7} and 3\sqrt{7} to get 7\sqrt{7}.

$$7\sqrt{7}-2\sqrt{232}$$

Factor 232=2^{2}\times 58. Rewrite the square root of the product \sqrt{2^{2}\times 58} as the product of square roots \sqrt{2^{2}}\sqrt{58}. Take the square root of 2^{2}.

$$7\sqrt{7}-2\times 2\sqrt{58}$$

Multiply -2 and 2 to get -4.

$$7\sqrt{7}-4\sqrt{58}$$