Solve 5sqrt{128}-3sqrt{50}

$$5 \sqrt { 128 } - 3 \sqrt { 50 }$$

Evaluate

$$25\sqrt{2}\approx 35.355339059$$

Solution Steps

Factor 128=8^{2}\times 2. Rewrite the square root of the product \sqrt{8^{2}\times 2} as the product of square roots \sqrt{8^{2}}\sqrt{2}. Take the square root of 8^{2}.

$$5\times 8\sqrt{2}-3\sqrt{50}$$

Multiply 5 and 8 to get 40.

$$40\sqrt{2}-3\sqrt{50}$$

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}.

$$40\sqrt{2}-3\times 5\sqrt{2}$$

Multiply -3 and 5 to get -15.

$$40\sqrt{2}-15\sqrt{2}$$

Combine 40\sqrt{2} and -15\sqrt{2} to get 25\sqrt{2}.

$$25\sqrt{2}$$