Question #bfe87

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Answer 1 · 2016-09-19T11:07:41

#+-2sqrt(3)#

You are looking for squared numbers that you can 'remove' from the square root

Known:#" "3xx4=12#

But 4 is the same as #2^2# so we can write 12 as #3xx2^2# giving:

#sqrt(3xx2^2)#

Take the #2^2# outside the square root giving:

#2sqrt(3)" "color(brown)( larr" part answer")#

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Observe that in taking the #2^2# out of the square root we have to apply #sqrt(2^2)=2#

Actually it is #+-2# as :#(-2)xx(-2)=(+2)xx(+2)=4#

So if you wish to be totally correct you would write:

#sqrt(12)=+-2sqrt(3)#