SOLUTION: "how do you simplify the radical, square root of 252"

Question 207332: "how do you simplify the radical, square root of 252"
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
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 252

Factors:
1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 63, 84, 126, 252

Notice how 36 is the largest perfect square, so lets factor 252 into 36*7

Start with the given expression

Factor 252 into 36*7

Break up the square roots using the identity

Take the square root of the perfect square 36 to get 6

So the expression simplifies to

In other words,
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