SOLUTION: Using the product property simplify the expression. 1.)the square root of 52

Question 176667: Using the product property simplify the
expression.
1.)the square root of 52
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 52

Factors:
1, 2, 4, 13, 26, 52

Notice how 4 is the largest perfect square, so lets factor 52 into 4*13

Factor 52 into 4*13

Break up the square roots using the identity

Take the square root of the perfect square 4 to get 2

So the expression simplifies to

----------------------------
Check:

Notice if we evaluate the square root of 52 with a calculator we get

and if we evaluate we get

This shows that . So this verifies our answer
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