Solve sqrt{8}+sqrt{32}+sqrt{18}

$$\sqrt { 8 } + \sqrt { 32 } + \sqrt { 18 }$$

Evaluate

$$9\sqrt{2}\approx 12.727922061$$

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}.

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

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}.

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

Combine 2\sqrt{2} and 4\sqrt{2} to get 6\sqrt{2}.

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

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}.

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

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

$$9\sqrt{2}$$