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

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

Evaluate

$$\sqrt{2}\approx 1.414213562$$

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}.

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

Multiply -3 and 2 to get -6.

$$-6\sqrt{2}+2\sqrt{8}+3\sqrt{2}$$

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}.

$$-6\sqrt{2}+2\times 2\sqrt{2}+3\sqrt{2}$$

Multiply 2 and 2 to get 4.

$$-6\sqrt{2}+4\sqrt{2}+3\sqrt{2}$$

Combine -6\sqrt{2} and 4\sqrt{2} to get -2\sqrt{2}.

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

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

$$\sqrt{2}$$