Question

How do you simplify `sqrt 8 /( 2 sqrt3)`?

Answer 1

`(sqrt8)/(2sqrt 3)=color(blue)((sqrt 6)/3)`

Explanation:

`(sqrt 8)/(2sqrt 3)`

Simplify `sqrt 8`.

`sqrt 8=sqrt(2xx2xx2)=sqrt(2^2xx 2)=2sqrt2`

Rewrite the fraction.

`(2sqrt2)/(2sqrt 3)`

Rationalize the denominator by multiplying the numerator and denominator by `sqrt 3`.

`(2sqrt2)/(2sqrt 3)xx(sqrt3)/(sqrt 3)`

Simplify.

`(2sqrt2sqrt3)/(2xx3)`

Simplify.

`(2sqrt6)/(2xx3)`

Simplify.

`(cancel2sqrt6)/(cancel2xx3)`

Simplify.

`(sqrt 6)/3`

Answer 2

`sqrt (2/3)`

Explanation:

`8=2^3`
`sqrt (8) = 2^(3/2)`

Therefore we have

`(2^(3/2).2^(-1))/sqrt (3)`

Add the exponent coefficients for 2

`(2^(1/2))/sqrt (3)`

Same as `sqrt(2/3)`

Answer 3

`sqrt(2/3)`

Explanation:

`sqrt8/(2sqrt3)`

We could see that

`sqrt8=sqrt(4*2)`

So

`=sqrt(4*2)/(2sqrt3_`

`=(cancel2sqrt2)/(cancel2sqrt3)`

`=sqrt2/sqrt3=sqrt(2/3)`

But wait ! We could not have irrational numbers in the denominator.

So,rationalize the denominator by multiplying with `sqrt3/sqrt3`

`sqrt2/sqrt3*sqrt3/sqrt3`

`=sqrt6/3`