Solve sqrt{5^2+5^2}+100^2

$$\sqrt { 5 ^ { 2 } + 5 ^ { 2 } } + 100 ^ { 2 }$$

Evaluate

$$5\left(\sqrt{2}+2000\right)\approx 10007.071067812$$

Solution Steps

Calculate 5 to the power of 2 and get 25.

$$\sqrt{25+5^{2}}+100^{2}$$

Calculate 5 to the power of 2 and get 25.

$$\sqrt{25+25}+100^{2}$$

Add 25 and 25 to get 50.

$$\sqrt{50}+100^{2}$$

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}.

$$5\sqrt{2}+100^{2}$$

Calculate 100 to the power of 2 and get 10000.

$$5\sqrt{2}+10000$$

Factor

$$5 {(\sqrt{2} + 2000)} = 10007.071067812$$