Solve 3sqrt{8}+2sqrt{2}-(sqrt{8}+sqrt{2})

$$3 \sqrt { 8 } + 2 \sqrt { 2 } - ( \sqrt { 8 } + \sqrt { 2 } )$$

Evaluate

$$5\sqrt{2}\approx 7.071067812$$

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}.

$$3\times 2\sqrt{2}+2\sqrt{2}-\left(\sqrt{8}+\sqrt{2}\right)$$

Multiply 3 and 2 to get 6.

$$6\sqrt{2}+2\sqrt{2}-\left(\sqrt{8}+\sqrt{2}\right)$$

Combine 6\sqrt{2} and 2\sqrt{2} to get 8\sqrt{2}.

$$8\sqrt{2}-\left(\sqrt{8}+\sqrt{2}\right)$$

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}.

$$8\sqrt{2}-\left(2\sqrt{2}+\sqrt{2}\right)$$

Combine 2\sqrt{2} and \sqrt{2} to get 3\sqrt{2}.

$$8\sqrt{2}-3\sqrt{2}$$

Combine 8\sqrt{2} and -3\sqrt{2} to get 5\sqrt{2}.

$$5\sqrt{2}$$