What is a square root?
The square root of 1616 is 44 because 4xx4 = 164×4=16
The square root of 99 is 33 because 3xx3 =93×3=9
In maths: sqrt49 = 7√49=7, because 7xx 7 = 7^2 = 497×7=72=49
The square root of a number is another number which, multiplied by itself gives the number.
2424 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√16=4and√25=5, so sqrt 24√24 will be just less than 5.
We look at the factors of 2424 which are 1, 2, 3, 4, 6, 8, 12, 241,2,3,4,6,8,12,24
Notice that only 1 and 41and4 are square numbers.
Write sqrt24√24 as factors which are squares:
" "(1 xx 24 (1×24 does not help at all!!)
sqrt24 = sqrt(4xx6) = sqrt4 xx sqrt6√24=√4×6=√4×√6
We can work out sqrt4√4, but not sqrt6√6:
color(red)(sqrt4 = 2)√4=2
Now, we have to work out: sqrt24/2√242
This is the same as: sqrt(4 xx 6)/2√4×62 which is also (color(red)(sqrt4) xx sqrt6)/2√4×√62
= (color(red)(2 )xx sqrt6)/2" "larr color(red)(sqrt4 = 2)=2×√62 ←√4=2
= (cancel2 xx sqrt6)/cancel2" "larr remember 2/2 = 1
=sqrt6
We cannot work this out, so leave it like this.
