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What is the simpliefied form of √96? Answer needs to be in radical form.

 

Please help :C and please show how to figure it out and the answer to it.. Thank you =^.^=

Guest Sep 1, 2014

Best Answer 

 #1
avatar+91491 
+5

$$\sqrt{96}$$

In order to simplify a surd you need to find a square number that goes into the number under the root.

If there is no square number factor then the surd cannot be simplified.

square numbers are 1,4,9,16,25,36,49,64,81....

Now 4 goes into 96 so lets use that one.

 

$$\sqrt{96}\\
=\sqrt{4*24}\\
=\sqrt4 * \sqrt{24}\\
=2*\sqrt{24}\\
=2\sqrt{24}\\$$

 

Now can this be simplified further?  4 is a square number and it is a factor of 24.  So we can do more!

 

$$2 *\sqrt{24}\\
=2*\sqrt{4*6}\\
=2*\sqrt{4} * \sqrt{6}\\
=2*2*\sqrt{6}\\
=4*\sqrt{6}\\
=4\sqrt{6}$$

 

Now can this be simplified further?  There are no square factors of 6 so this is finished!

 

NOTE:  If you had noticed that 16, which is a square number, is also a factor of 96 this could have been done more quickly.

$$\sqrt{96}\\
=\sqrt{16*6}\\
=\sqrt{16}*\sqrt{6}\\
=4*\sqrt{6}\\
=4\sqrt{6}\\$$

 

so if you find the Biggest square number to start with then it is quicker but if you find a smaller one you will still get there eventually.   

Melody  Sep 1, 2014
Sort: 

1+0 Answers

 #1
avatar+91491 
+5
Best Answer

$$\sqrt{96}$$

In order to simplify a surd you need to find a square number that goes into the number under the root.

If there is no square number factor then the surd cannot be simplified.

square numbers are 1,4,9,16,25,36,49,64,81....

Now 4 goes into 96 so lets use that one.

 

$$\sqrt{96}\\
=\sqrt{4*24}\\
=\sqrt4 * \sqrt{24}\\
=2*\sqrt{24}\\
=2\sqrt{24}\\$$

 

Now can this be simplified further?  4 is a square number and it is a factor of 24.  So we can do more!

 

$$2 *\sqrt{24}\\
=2*\sqrt{4*6}\\
=2*\sqrt{4} * \sqrt{6}\\
=2*2*\sqrt{6}\\
=4*\sqrt{6}\\
=4\sqrt{6}$$

 

Now can this be simplified further?  There are no square factors of 6 so this is finished!

 

NOTE:  If you had noticed that 16, which is a square number, is also a factor of 96 this could have been done more quickly.

$$\sqrt{96}\\
=\sqrt{16*6}\\
=\sqrt{16}*\sqrt{6}\\
=4*\sqrt{6}\\
=4\sqrt{6}\\$$

 

so if you find the Biggest square number to start with then it is quicker but if you find a smaller one you will still get there eventually.   

Melody  Sep 1, 2014

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