Solve (sqrt{8}+2sqrt{7}+sqrt{8}-2sqrt{7})

$$( \sqrt { 8 } + 2 \sqrt { 7 } + \sqrt { 8 } - 2 \sqrt { 7 } )$$

Evaluate

$$4\sqrt{2}\approx 5.656854249$$

Solution Steps

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

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

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

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

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

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

Combine 2\sqrt{7} and -2\sqrt{7} to get 0.

$$4\sqrt{2}$$