Solve 3sqrt{18}-sqrt{72}+2sqrt{8}

$$3 \sqrt { 18 } - \sqrt { 72 } + 2 \sqrt { 8 }$$

Evaluate

$$7\sqrt{2}\approx 9.899494937$$

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}.

$$3\times 3\sqrt{2}-\sqrt{72}+2\sqrt{8}$$

Multiply 3 and 3 to get 9.

$$9\sqrt{2}-\sqrt{72}+2\sqrt{8}$$

Factor 72=6^{2}\times 2. Rewrite the square root of the product \sqrt{6^{2}\times 2} as the product of square roots \sqrt{6^{2}}\sqrt{2}. Take the square root of 6^{2}.

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

Combine 9\sqrt{2} and -6\sqrt{2} to get 3\sqrt{2}.

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

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}.

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

Multiply 2 and 2 to get 4.

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

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

$$7\sqrt{2}$$