How do you simplify square root of 24 divided by 2?

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Answer 1 · 2015-09-19T22:40:31

$sqrt(24)/2 = sqrt(6)$

$sqrt(24)/2 = sqrt(4*6)/2 =(sqrt(4)sqrt(6))/2 =(2sqrt(6))/2 =sqrt(6)$

Answer 2 · 2017-03-17T11:58:43

$sqrt6$

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.