SOLUTION: If √96 is simplified to a√b such that a and b are integers, what is the value of a? √ = Radical sign Thank you, in advance.

Algebra ->  Radicals -> SOLUTION: If √96 is simplified to a√b such that a and b are integers, what is the value of a? √ = Radical sign Thank you, in advance.      Log On


   

Question 139576: If √96 is simplified to a√b such that a and b are integers, what is the value of a?
√ = Radical sign
Thank you, in advance.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%2896%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 96


Factors:
1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96


Notice how 16 is the largest perfect square, so lets factor 96 into 16*6


sqrt%2816%2A6%29 Factor 96 into 16*6

sqrt%2816%29%2Asqrt%286%29 Break up the square roots using the identity sqrt%28x%2Ay%29=sqrt%28x%29%2Asqrt%28y%29

4%2Asqrt%286%29 Take the square root of the perfect square 16 to get 4

So the expression sqrt%2896%29 simplifies to 4%2Asqrt%286%29


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Answer:
So in this case, the value of a=4





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Check:
Notice if we evaluate the square root of 96 with a calculator we get

sqrt%2896%29=9.79795897113271

and if we evaluate 4%2Asqrt%286%29 we get

4%2Asqrt%286%29=9.79795897113271

This shows that sqrt%2896%29=4%2Asqrt%286%29. So this verifies our answer