Solve 3sqrt{18}-sqrt{8}+2sqrt{32}

$$3 \sqrt { 18 } - \sqrt { 8 } + 2 \sqrt { 32 }$$

Evaluate

$$15\sqrt{2}\approx 21.213203436$$

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}.

$$3\times 3\sqrt{2}-\sqrt{8}+2\sqrt{32}$$

Multiply 3 and 3 to get 9.

$$9\sqrt{2}-\sqrt{8}+2\sqrt{32}$$

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}.

$$9\sqrt{2}-2\sqrt{2}+2\sqrt{32}$$

Combine 9\sqrt{2} and -2\sqrt{2} to get 7\sqrt{2}.

$$7\sqrt{2}+2\sqrt{32}$$

Factor 32=4^{2}\times 2. Rewrite the square root of the product \sqrt{4^{2}\times 2} as the product of square roots \sqrt{4^{2}}\sqrt{2}. Take the square root of 4^{2}.

$$7\sqrt{2}+2\times 4\sqrt{2}$$

Multiply 2 and 4 to get 8.

$$7\sqrt{2}+8\sqrt{2}$$

Combine 7\sqrt{2} and 8\sqrt{2} to get 15\sqrt{2}.

$$15\sqrt{2}$$