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\sqrt{100\times 10}
Calculate the square root of 100 and get 10.
\sqrt{1000}
Multiply 100 and 10 to get 1000.
10\sqrt{10}
Factor 1000=10^{2}\times 10. Rewrite the square root of the product \sqrt{10^{2}\times 10} as the product of square roots \sqrt{10^{2}}\sqrt{10}. Take the square root of 10^{2}.