1000's square route

1000 is close to 1024, which is $2^{10}$ or $(2^5)^2$ $\sqrt{1000}\approx\sqrt{1024}=\sqrt{(2^5)^2}=2^5=32$ $\therefore \sqrt{1000}$ must be slightly less than 32. The only option slightly less than 32 is 31.62277660...

Use a calculator.