What is a square root?
The square root of #16# is #4# because #4xx4 = 16#
The square root of #9# is #3# because #3xx3 =9#
In maths: #sqrt49 = 7#, because #7xx 7 = 7^2 = 49#
The square root of a number is another number which, multiplied by itself gives the number.
#24# is not a square number because it does not have an exact square root. We cannot find the exact answer for it.
#sqrt16 = 4 and sqrt25 = 5#, so #sqrt 24# will be just less than 5.
We look at the factors of #24# which are #1, 2, 3, 4, 6, 8, 12, 24#
Notice that only #1 and 4# are square numbers.
Write #sqrt24# as factors which are squares:
#" "(1 xx 24# does not help at all!!)
#sqrt24 = sqrt(4xx6) = sqrt4 xx sqrt6#
We can work out #sqrt4#, but not #sqrt6#:
#color(red)(sqrt4 = 2)#
Now, we have to work out: #sqrt24/2#
This is the same as: #sqrt(4 xx 6)/2# which is also #(color(red)(sqrt4) xx sqrt6)/2#
#= (color(red)(2 )xx sqrt6)/2" "larr color(red)(sqrt4 = 2)#
#= (cancel2 xx sqrt6)/cancel2" "larr# remember #2/2 = 1#
#=sqrt6#
We cannot work this out, so leave it like this.
