Solve sqrt{10000+1000^2}

$$\sqrt{ 10000+ { 1000 }^{ 2 } }$$

Evaluate

$$100\sqrt{101}\approx 1004.987562112$$

Solution Steps

Calculate 1000 to the power of 2 and get 1000000.

$$\sqrt{10000+1000000}$$

Add 10000 and 1000000 to get 1010000.

$$\sqrt{1010000}$$

Factor 1010000=100^{2}\times 101. Rewrite the square root of the product \sqrt{100^{2}\times 101} as the product of square roots \sqrt{100^{2}}\sqrt{101}. Take the square root of 100^{2}.

$$100\sqrt{101}$$