Solve sqrt{8}+3sqrt{50}-sqrt{2}

$$\sqrt{ 8 } +3 \sqrt{ 50 } - \sqrt{ 2 }$$

Evaluate

$$16\sqrt{2}\approx 22.627416998$$

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}.

$$2\sqrt{2}+3\sqrt{50}-\sqrt{2}$$

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}.

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

Multiply 3 and 5 to get 15.

$$2\sqrt{2}+15\sqrt{2}-\sqrt{2}$$

Combine 2\sqrt{2} and 15\sqrt{2} to get 17\sqrt{2}.

$$17\sqrt{2}-\sqrt{2}$$

Combine 17\sqrt{2} and -\sqrt{2} to get 16\sqrt{2}.

$$16\sqrt{2}$$