Question 217291: My brother in law is taking some courses, and asked me about this problem.
Please solve this equation, and show how you did so. 
I know that there is a way to show how the sqrt25344 equals the other side, but the book he's using seems to be skipping a step on how they got part of the answer.
Thanks,
Dave
Found 2 solutions by jim_thompson5910, stanbon:
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 25344
Factors:
1, 2, 3, 4, 6, 8, 9, 11, 12, 16, 18, 22, 24, 32, 33, 36, 44, 48, 64, 66, 72, 88, 96, 99, 128, 132, 144, 176, 192, 198, 256, 264, 288, 352, 384, 396, 528, 576, 704, 768, 792, 1056, 1152, 1408, 1584, 2112, 2304, 2816, 3168, 4224, 6336, 8448, 12672, 25344
Notice how 2304 is the largest perfect square, so lets factor 25344 into 2304*11
 Factor 25344 into 2304*11
 Break up the square roots using the identity 
 Take the square root of the perfect square 2304 to get 48
So the expression simplifies to
In other words, 
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Check:
Notice if we evaluate the square root of 25344 with a calculator we get
and if we evaluate we get
This shows that . So this verifies our answer
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! sqrt25344 = 48sqrt11
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25344 = 2304*11
25344 = 48^2*11
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sqrt(25344) = sqrt(48^2*11)
= sqrt(48^2)*sqrt(11)
= 48*sqrt(11)
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Cheers,
Stan H.
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