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10\sqrt{10}=\sqrt{x}
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}.
\sqrt{x}=10\sqrt{10}
Swap sides so that all variable terms are on the left hand side.
x=1000
Square both sides of the equation.