Solve sqrt{32}-sqrt{8}+sqrt{72}

$$\sqrt { 32 } - \sqrt { 8 } + \sqrt { 72 }$$

Evaluate

$$8\sqrt{2}\approx 11.313708499$$

Solution Steps

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}.

$$4\sqrt{2}-\sqrt{8}+\sqrt{72}$$

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}.

$$4\sqrt{2}-2\sqrt{2}+\sqrt{72}$$

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

$$2\sqrt{2}+\sqrt{72}$$

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}.

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

Combine 2\sqrt{2} and 6\sqrt{2} to get 8\sqrt{2}.

$$8\sqrt{2}$$