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

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Question 176667: Using the product property simplify the
expression.
1.)the square root of 52
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

sqrt%2852%29 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


sqrt%284%2A13%29 Factor 52 into 4*13


sqrt%284%29%2Asqrt%2813%29 Break up the square roots using the identity sqrt%28x%2Ay%29=sqrt%28x%29%2Asqrt%28y%29


2%2Asqrt%2813%29 Take the square root of the perfect square 4 to get 2


So the expression sqrt%2852%29 simplifies to 2%2Asqrt%2813%29

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Check:

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

sqrt%2852%29=7.21110255092798

and if we evaluate 2%2Asqrt%2813%29 we get

2%2Asqrt%2813%29=7.21110255092798

This shows that sqrt%2852%29=2%2Asqrt%2813%29. So this verifies our answer