 Start with the given expression
The goal of simplifying expressions with square roots is to factor the radicand into a product of two numbers. One of these two numbers must be a perfect square. When you take the square root of this perfect square, you will get a rational number.
So let's list the factors of 500
Factors:
1, 2, 4, 5, 10, 20, 25, 50, 100, 125, 250, 500
Notice how 100 is the largest perfect square, so lets factor 500 into 100*5
 Factor 500 into 100*5
 Break up the square roots using the identity 
 Take the square root of the perfect square 100 to get 10
So the expression simplifies to
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Check:
Notice if we evaluate the square root of 500 with a calculator we get
and if we evaluate we get
This shows that  . So this verifies our answer |
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