Question 115070: radical 6000
Found 2 solutions by checkley71, jim_thompson5910:
Answer by checkley71(8403)   (Show Source):
Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!  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 6000
Factors:
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 40, 48, 50, 60, 75, 80, 100, 120, 125, 150, 200, 240, 250, 300, 375, 400, 500, 600, 750, 1000, 1200, 1500, 2000, 3000, 6000
Notice how 400 is the largest perfect square, so lets factor 6000 into 400*15
 Factor 6000 into 400*15
 Break up the square roots using the identity 
 Take the square root of the perfect square 400 to get 20
So the expression simplifies to
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Check:
Notice if we evaluate the square root of 6000 with a calculator we get
and if we evaluate we get
This shows that  . So this verifies our answer
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