Solve sqrt{7}-sqrt{28}+2sqrt{63}-10sqrt{7}

$$\sqrt { 7 } - \sqrt { 28 } + 2 \sqrt { 63 } - 10 \sqrt { 7 }$$

Evaluate

$$-5\sqrt{7}\approx -13.228756555$$

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}.

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

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

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

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}.

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

Multiply 2 and 3 to get 6.

$$-\sqrt{7}+6\sqrt{7}-10\sqrt{7}$$

Combine -\sqrt{7} and 6\sqrt{7} to get 5\sqrt{7}.

$$5\sqrt{7}-10\sqrt{7}$$

Combine 5\sqrt{7} and -10\sqrt{7} to get -5\sqrt{7}.

$$-5\sqrt{7}$$