Solve sqrt{28}+2sqrt{175}-3sqrt{63}=

$$\sqrt { 28 } + 2 \sqrt { 175 } - 3 \sqrt { 63 } =$$

Evaluate

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

Solution Steps

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}.

$$2\sqrt{7}+2\sqrt{175}-3\sqrt{63}$$

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}.

$$2\sqrt{7}+2\times 5\sqrt{7}-3\sqrt{63}$$

Multiply 2 and 5 to get 10.

$$2\sqrt{7}+10\sqrt{7}-3\sqrt{63}$$

Combine 2\sqrt{7} and 10\sqrt{7} to get 12\sqrt{7}.

$$12\sqrt{7}-3\sqrt{63}$$

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}.

$$12\sqrt{7}-3\times 3\sqrt{7}$$

Multiply -3 and 3 to get -9.

$$12\sqrt{7}-9\sqrt{7}$$

Combine 12\sqrt{7} and -9\sqrt{7} to get 3\sqrt{7}.

$$3\sqrt{7}$$