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.

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) (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 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

Factor 96 into 16*6

Break up the square roots using the identity

Take the square root of the perfect square 16 to get 4

So the expression simplifies to

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Answer:
So in this case, the value of

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

and if we evaluate we get

This shows that . So this verifies our answer
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SOLUTION: If &#8730;96 is simplified to a&#8730;b such that a and b are integers, what is the value of a? &#8730; = Radical sign Thank you, in advance.

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.