#1**+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.

Melody
Apr 10, 2015

#1**+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