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how do i rewrite in simplest radical form or as a rational number

 Apr 9, 2015

Best Answer 

 #1
avatar+95361 
+5

Lets try to simplify    $$\sqrt{162}$$

 

I have to look for a squared number that goes into 162

1^1=1     that doesn't help, every number can be divided by 1

2^2=4     no, doesn't go iinto 163

3^2=9     bingo!  9 goes into 162    18 times

 

$$\\\sqrt{162}\\=\sqr{9*18}\\=\sqrt9*\sqrt{18}\\=3*\sqrt{18}\\$$

 

now 9 will go into 18 too.    9*2=18

 

$$\\3*\sqrt{18}\\=3*\sqrt{9*2}\\=3*\sqrt{9}*\sqrt{2\\}=3*3*\sqrt2\\=9\sqrt2$$

 

And that is how it is done.  If the number under the square root is not divisable by any squared number then the surd cannot be simplified.   

 Apr 10, 2015
 #1
avatar+95361 
+5
Best Answer

Lets try to simplify    $$\sqrt{162}$$

 

I have to look for a squared number that goes into 162

1^1=1     that doesn't help, every number can be divided by 1

2^2=4     no, doesn't go iinto 163

3^2=9     bingo!  9 goes into 162    18 times

 

$$\\\sqrt{162}\\=\sqr{9*18}\\=\sqrt9*\sqrt{18}\\=3*\sqrt{18}\\$$

 

now 9 will go into 18 too.    9*2=18

 

$$\\3*\sqrt{18}\\=3*\sqrt{9*2}\\=3*\sqrt{9}*\sqrt{2\\}=3*3*\sqrt2\\=9\sqrt2$$

 

And that is how it is done.  If the number under the square root is not divisable by any squared number then the surd cannot be simplified.   

Melody Apr 10, 2015

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