Simplify $\sqrt{25000}$.
We have:

$\sqrt{25000}=\sqrt{2500\cdot 10}=\boxed{50\sqrt{10}}$.
50\sqrt{10}
Level 4
Prealgebra
Problem: Simplify $\sqrt{25000}$.
Solution:<|START_OF_LATENT|><|PRIOR_PREFIX|>To simplify $\sqrt{25000}$, first factor 25000 into its prime components. Recognize that 25000 can be expressed as $250 \times 100$. Next, simplify each component: $100 = 10^2$ and $250 = 25 \times 10$. Since $25 = 5^2$, we can rewrite 25000 as $5^2 \times 10^3$. 

Now, express this in terms of square roots: $\sqrt{25000} = \sqrt{5^2 \times 10^3}$. Using the property of square roots that states $\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}$, we can separate the terms: $\sqrt{25000} = \sqrt{5^2} \times \sqrt{10^3}$. 

Calculating the square roots gives us $\sqrt{5^2} = 5$ and $\sqrt{10^3} = \sqrt{10^2 \times 10} = 10\sqrt{10}$. 

Now, combine these results: $5 \times 10\sqrt{10} = 50\sqrt{10}$. 

Thus, the final answer is $50\sqrt{10}$.<|END_OF_LATENT|> The final answer is $50\sqrt{10}$.