Solve 10sqrt{2}+sqrt{8}+sqrt{50}

$$10 \sqrt { 2 } + \sqrt { 8 } + \sqrt { 50 }$$

Evaluate

$$17\sqrt{2}\approx 24.04163056$$

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}.

$$10\sqrt{2}+2\sqrt{2}+\sqrt{50}$$

Combine 10\sqrt{2} and 2\sqrt{2} to get 12\sqrt{2}.

$$12\sqrt{2}+\sqrt{50}$$

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}.

$$12\sqrt{2}+5\sqrt{2}$$

Combine 12\sqrt{2} and 5\sqrt{2} to get 17\sqrt{2}.

$$17\sqrt{2}$$