Solve frac{sqrt{20^2+2^2}}{2}

$$\frac { \sqrt { 20 ^ { 2 } + 2 ^ { 2 } } } { 2 }$$

Evaluate

$$\sqrt{101}\approx 10.049875621$$

Solution Steps

Calculate 20 to the power of 2 and get 400.

$$\frac{\sqrt{400+2^{2}}}{2}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{\sqrt{400+4}}{2}$$

Add 400 and 4 to get 404.

$$\frac{\sqrt{404}}{2}$$

Factor 404=2^{2}\times 101. Rewrite the square root of the product \sqrt{2^{2}\times 101} as the product of square roots \sqrt{2^{2}}\sqrt{101}. Take the square root of 2^{2}.

$$\frac{2\sqrt{101}}{2}$$

Cancel out 2 and 2.

$$\sqrt{101}$$