Solve sqrt{8}+sqrt{72}+sqrt{50}

$$\sqrt { 8 } + \sqrt { 72 } + \sqrt { 50 }$$

Evaluate

$$13\sqrt{2}\approx 18.384776311$$

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}.

$$2\sqrt{2}+\sqrt{72}+\sqrt{50}$$

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}.

$$2\sqrt{2}+6\sqrt{2}+\sqrt{50}$$

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

$$8\sqrt{2}+\sqrt{50}$$

Factor 50=5^{2}\times 2. Rewrite the square root of the product \sqrt{5^{2}\times 2} as the product of square roots \sqrt{5^{2}}\sqrt{2}. Take the square root of 5^{2}.

$$8\sqrt{2}+5\sqrt{2}$$

Combine 8\sqrt{2} and 5\sqrt{2} to get 13\sqrt{2}.

$$13\sqrt{2}$$