Solve sqrt{63}+2sqrt{28}-sqrt{175}

$$\sqrt { 63 } + 2 \sqrt { 28 } - \sqrt { 175 }$$

Evaluate

$$2\sqrt{7}\approx 5.291502622$$

Solution Steps

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}.

$$3\sqrt{7}+2\sqrt{28}-\sqrt{175}$$

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}.

$$3\sqrt{7}+2\times 2\sqrt{7}-\sqrt{175}$$

Multiply 2 and 2 to get 4.

$$3\sqrt{7}+4\sqrt{7}-\sqrt{175}$$

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

$$7\sqrt{7}-\sqrt{175}$$

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}.

$$7\sqrt{7}-5\sqrt{7}$$

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

$$2\sqrt{7}$$