Solve 6sqrt{18}+2sqrt{32}

$$6 \sqrt { 18 } + 2 \sqrt { 32 }$$

Evaluate

$$26\sqrt{2}\approx 36.769552622$$

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}.

$$6\times 3\sqrt{2}+2\sqrt{32}$$

Multiply 6 and 3 to get 18.

$$18\sqrt{2}+2\sqrt{32}$$

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}.

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

Multiply 2 and 4 to get 8.

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

Combine 18\sqrt{2} and 8\sqrt{2} to get 26\sqrt{2}.

$$26\sqrt{2}$$