*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

#1**+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

#1**+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