Solve sqrt{50}+2sqrt{18}

$$\sqrt { 50 } + 2 \sqrt { 18 }$$

Evaluate

$$11\sqrt{2}\approx 15.556349186$$

Solution Steps

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}.

$$5\sqrt{2}+2\sqrt{18}$$

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}.

$$5\sqrt{2}+2\times 3\sqrt{2}$$

Multiply 2 and 3 to get 6.

$$5\sqrt{2}+6\sqrt{2}$$

Combine 5\sqrt{2} and 6\sqrt{2} to get 11\sqrt{2}.

$$11\sqrt{2}$$