Solve sqrt{24^2-20^2}

$$\sqrt { 24 ^ { 2 } - 20 ^ { 2 } }$$

Evaluate

$$4\sqrt{11}\approx 13.266499161$$

Solution Steps

Calculate 24 to the power of 2 and get 576.

$$\sqrt{576-20^{2}}$$

Calculate 20 to the power of 2 and get 400.

$$\sqrt{576-400}$$

Subtract 400 from 576 to get 176.

$$\sqrt{176}$$

Factor 176=4^{2}\times 11. Rewrite the square root of the product \sqrt{4^{2}\times 11} as the product of square roots \sqrt{4^{2}}\sqrt{11}. Take the square root of 4^{2}.

$$4\sqrt{11}$$