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

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.