Solve 3sqrt{18}-5sqrt{2}+6sqrt{8}

$$3 \sqrt { 18 } - 5 \sqrt { 2 } + 6 \sqrt { 8 }$$

Evaluate

$$16\sqrt{2}\approx 22.627416998$$

Solution Steps

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}.

$$3\times 3\sqrt{2}-5\sqrt{2}+6\sqrt{8}$$

Multiply 3 and 3 to get 9.

$$9\sqrt{2}-5\sqrt{2}+6\sqrt{8}$$

Combine 9\sqrt{2} and -5\sqrt{2} to get 4\sqrt{2}.

$$4\sqrt{2}+6\sqrt{8}$$

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}.

$$4\sqrt{2}+6\times 2\sqrt{2}$$

Multiply 6 and 2 to get 12.

$$4\sqrt{2}+12\sqrt{2}$$

Combine 4\sqrt{2} and 12\sqrt{2} to get 16\sqrt{2}.

$$16\sqrt{2}$$