Question 139576
{{{sqrt(96)}}} 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(16*6)}}} Factor 96 into 16*6
 
{{{sqrt(16)*sqrt(6)}}} Break up the square roots using the identity {{{sqrt(x*y)=sqrt(x)*sqrt(y)}}}
 
{{{4*sqrt(6)}}} Take the square root of the perfect square 16 to get 4 
 
So the expression {{{sqrt(96)}}} simplifies to {{{4*sqrt(6)}}}



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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(96)=9.79795897113271}}}


and if we evaluate {{{4*sqrt(6)}}} we get


{{{4*sqrt(6)=9.79795897113271}}}


This shows that {{{sqrt(96)=4*sqrt(6)}}}. So this verifies our answer