Solve sqrt{400*42-80^2}

$$\sqrt { 400 \times 42 - 80 ^ { 2 } }$$

Evaluate

$$20\sqrt{26}\approx 101.980390272$$

Solution Steps

Multiply 400 and 42 to get 16800.

$$\sqrt{16800-80^{2}}$$

Calculate 80 to the power of 2 and get 6400.

$$\sqrt{16800-6400}$$

Subtract 6400 from 16800 to get 10400.

$$\sqrt{10400}$$

Factor 10400=20^{2}\times 26. Rewrite the square root of the product \sqrt{20^{2}\times 26} as the product of square roots \sqrt{20^{2}}\sqrt{26}. Take the square root of 20^{2}.

$$20\sqrt{26}$$