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how do you simplify the square root of 24?

 Oct 9, 2017
 #1
avatar+232 
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i dont think you can

 Oct 9, 2017
 #2
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So its a surd?
 

Guest Oct 9, 2017
 #5
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Yes, the square root of any number that is not a perfect square is irrational, which is also known as a surd.

 

For example, \(\sqrt{4}\) is rational because the radicand is a perfect square while \(\sqrt{8}\) is irrational because the radicand is not a perfect square.

TheXSquaredFactor  Oct 9, 2017
edited by TheXSquaredFactor  Oct 9, 2017
edited by TheXSquaredFactor  Oct 9, 2017
 #3
avatar+5259 
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The square root of 24 comes out to a complicated decimal, so the simplest it can be is square root of 24.

 Oct 9, 2017
 #4
avatar+2338 
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By simplification, I think the user wants to determine the simplest radical form of \(\sqrt{24}\)

 

The first step is to find a perfect square that is also a factor of the radicand. The radicand, in case you are wondering, is the number or expression underneath the square root symbol. The factors of 24 are 1,2,3,4,6,8,12,24

 

The 4 is bolded because it is a factor of 24 and also a perfect square.

 

\(\sqrt{24}=\sqrt{4*6}=\sqrt{4}\sqrt{6}\)

 

As you can see, the square root of 4 simplifies to 2. \(\sqrt{24}=2\sqrt{6}\)

.
 Oct 9, 2017

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