### Instruction: Simplify $\sqrt{25000}$.### Response: I want to simplify the square root of 25000 by finding the largest perfect square that divides 25000 evenly.
I know that 100 is a perfect square, and it divides 25000 evenly, since 25000 = 100 * 250.
So I can rewrite $\sqrt{25000}$ as $\sqrt{100 * 250}$.
Then I can use the property of square roots that says $\sqrt{ab} = \sqrt{a} * \sqrt{b}$ for any positive numbers a and b.
So $\sqrt{100 * 250} = \sqrt{100} * \sqrt{250}$.
I know that $\sqrt{100} = 10$, since 10 * 10 = 100.
So now I have $\sqrt{25000} = 10 * \sqrt{250}$.
I can simplify $\sqrt{250}$ further by finding another perfect square that divides 250 evenly.
I know that 25 is a perfect square, and it divides 250 evenly, since 250 = 25 * 10.
So I can rewrite $\sqrt{250}$ as $\sqrt{25 * 10}$.
Then I can use the same property of square roots to get $\sqrt{25 * 10} = \sqrt{25} * \sqrt{10}$.
I know that $\sqrt{25} = 5$, since 5 * 5 = 25.
So now I have $\sqrt{25000} = 10 * \sqrt{250} = 10 * 5 * \sqrt{10}$.
I can simplify this further by multiplying 10 and 5 to get 50.