Solve sqrt{8}+5sqrt{2}-7sqrt{50}

$$\sqrt { 8 } + 5 \sqrt { 2 } - 7 \sqrt { 50 }$$

Evaluate

$$-28\sqrt{2}\approx -39.597979746$$

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}.

$$2\sqrt{2}+5\sqrt{2}-7\sqrt{50}$$

Combine 2\sqrt{2} and 5\sqrt{2} to get 7\sqrt{2}.

$$7\sqrt{2}-7\sqrt{50}$$

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}.

$$7\sqrt{2}-7\times 5\sqrt{2}$$

Multiply -7 and 5 to get -35.

$$7\sqrt{2}-35\sqrt{2}$$

Combine 7\sqrt{2} and -35\sqrt{2} to get -28\sqrt{2}.

$$-28\sqrt{2}$$