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

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

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}.

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

Multiply 3 and 2 to get 6.

$$\sqrt{2}+6\sqrt{2}-\sqrt{18}$$

Combine \sqrt{2} and 6\sqrt{2} to get 7\sqrt{2}.

$$7\sqrt{2}-\sqrt{18}$$

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}.

$$7\sqrt{2}-3\sqrt{2}$$

Combine 7\sqrt{2} and -3\sqrt{2} to get 4\sqrt{2}.

$$4\sqrt{2}$$