Solve sqrt{125}+sqrt{25}+sqrt{50}

$$\sqrt { 125 } + \sqrt { 25 } + \sqrt { 50 }$$

Evaluate

$$5\left(\sqrt{2}+\sqrt{5}+1\right)\approx 23.251407699$$

Solution Steps

Factor 125=5^{2}\times 5. Rewrite the square root of the product \sqrt{5^{2}\times 5} as the product of square roots \sqrt{5^{2}}\sqrt{5}. Take the square root of 5^{2}.

$$5\sqrt{5}+\sqrt{25}+\sqrt{50}$$

Calculate the square root of 25 and get 5.

$$5\sqrt{5}+5+\sqrt{50}$$

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}.

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