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.