Solve sqrt{10000+900^2}

$$\sqrt{ 10000+ { 900 }^{ 2 } }$$

Evaluate

$$100\sqrt{82}\approx 905.538513814$$

Solution Steps

Calculate 900 to the power of 2 and get 810000.

$$\sqrt{10000+810000}$$

Add 10000 and 810000 to get 820000.

$$\sqrt{820000}$$

Factor 820000=100^{2}\times 82. Rewrite the square root of the product \sqrt{100^{2}\times 82} as the product of square roots \sqrt{100^{2}}\sqrt{82}. Take the square root of 100^{2}.

$$100\sqrt{82}$$