Solve sqrt{28}+sqrt{14}+2sqrt{7}-3sqrt{63}):sqrt{7}

$$\sqrt { 28 } + \sqrt { 14 } + 2 \sqrt { 7 } - 3 \sqrt { 63 } ) : \sqrt { 7 }$$

Evaluate

$$\sqrt{14}-5\sqrt{7}\approx -9.487099169$$

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}.

$$2\sqrt{7}+\sqrt{14}+2\sqrt{7}-3\sqrt{63}$$

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

$$4\sqrt{7}+\sqrt{14}-3\sqrt{63}$$

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}.

$$4\sqrt{7}+\sqrt{14}-3\times 3\sqrt{7}$$

Multiply -3 and 3 to get -9.

$$4\sqrt{7}+\sqrt{14}-9\sqrt{7}$$

Combine 4\sqrt{7} and -9\sqrt{7} to get -5\sqrt{7}.

$$-5\sqrt{7}+\sqrt{14}$$