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# how do you simplify the square root of 24?

0
1764
5

how do you simplify the square root of 24?

Oct 9, 2017

#1
+232
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i dont think you can

Oct 9, 2017
#2
0

So its a surd?

Guest Oct 9, 2017
#5
+2338
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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
+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
+2338
+1

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. $$\sqrt{24}=2\sqrt{6}$$

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Oct 9, 2017