Solve -2sqrt{112}+2sqrt{28}+4sqrt{7}

$$- 2 \sqrt { 112 } + 2 \sqrt { 28 } + 4 \sqrt { 7 }$$

Evaluate

$$0$$

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}.

$$-2\times 4\sqrt{7}+2\sqrt{28}+4\sqrt{7}$$

Multiply -2 and 4 to get -8.

$$-8\sqrt{7}+2\sqrt{28}+4\sqrt{7}$$

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}.

$$-8\sqrt{7}+2\times 2\sqrt{7}+4\sqrt{7}$$

Multiply 2 and 2 to get 4.

$$-8\sqrt{7}+4\sqrt{7}+4\sqrt{7}$$

Combine -8\sqrt{7} and 4\sqrt{7} to get -4\sqrt{7}.

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

Combine -4\sqrt{7} and 4\sqrt{7} to get 0.

$$0$$

Factor

$$0$$