SOLUTION: My brother in law is taking some courses, and asked me about this problem. Please solve this equation, and show how you did so. {{{sqrt25344 = 48sqrt11}}} I know that th

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,

----------------------------
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
---------------------------------
25344 = 2304*11
25344 = 48^2*11
-------------------------
sqrt(25344) = sqrt(48^2*11)
= sqrt(48^2)*sqrt(11)
= 48*sqrt(11)
=============================
Cheers,
Stan H.
RELATED QUESTIONS
Could you help me to understand the complex numbers formulas and specially their signs?... (answered by ptaylor)
Please help me solve this application of systems of linear equations problem: Each... (answered by ankor@dixie-net.com,cahlove)
I have to use the quadratic formula to solve this equation. I have successfully completed (answered by jim_thompson5910)
I am having trouble with a question from my school text book and I have asked my teacher... (answered by checkley75,jim_thompson5910)
in my math class we're doing "problem solving and polynomials" and i do not have any idea (answered by richard1234,ewatrrr)
I am a frustrated father who was asked this question by my daughter. She does not know... (answered by ankor@dixie-net.com)
I could not find any lessons for my brother on Adding and Subtracting algebraic... (answered by AnlytcPhil)
Let me tell you why I am Using this site, Today I was taking my test and had no CLUEE on... (answered by stanbon)
I am having a hard time on how to start solving this problem. It was one of my extra... (answered by Alan3354)