Solve 7sqrt{2}-3sqrt{8}+4sqrt{18}

$$7 \sqrt{ 2 } -3 \sqrt{ 8 } +4 \sqrt{ 18 }$$

Evaluate

$$13\sqrt{2}\approx 18.384776311$$

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}.

$$7\sqrt{2}-3\times 2\sqrt{2}+4\sqrt{18}$$

Multiply -3 and 2 to get -6.

$$7\sqrt{2}-6\sqrt{2}+4\sqrt{18}$$

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

$$\sqrt{2}+4\sqrt{18}$$

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}.

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

Multiply 4 and 3 to get 12.

$$\sqrt{2}+12\sqrt{2}$$

Combine \sqrt{2} and 12\sqrt{2} to get 13\sqrt{2}.

$$13\sqrt{2}$$