Solve 3sqrt{2}-4sqrt{8}+2sqrt{18}

$$3 \sqrt { 2 } - 4 \sqrt { 8 } + 2 \sqrt { 18 }$$

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}.

$$3\sqrt{2}-4\times 2\sqrt{2}+2\sqrt{18}$$

Multiply -4 and 2 to get -8.

$$3\sqrt{2}-8\sqrt{2}+2\sqrt{18}$$

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

$$-5\sqrt{2}+2\sqrt{18}$$

Factor 18=3^{2}\times 2. Rewrite the square root of the product \sqrt{3^{2}\times 2} as the product of square roots \sqrt{3^{2}}\sqrt{2}. Take the square root of 3^{2}.

$$-5\sqrt{2}+2\times 3\sqrt{2}$$

Multiply 2 and 3 to get 6.

$$-5\sqrt{2}+6\sqrt{2}$$

Combine -5\sqrt{2} and 6\sqrt{2} to get \sqrt{2}.

$$\sqrt{2}$$