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

Guest Sep 1, 2014

#1
+91432
+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
+91432
+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

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