Question

How do you simplify `(8sqrt3 )/ sqrt6`?

Answer 1

`8/sqrt(2)`

Explanation:

Recall that `sqrta/sqrtb=sqrt(a/b)`

So, we're looking to simplify `8sqrt(3/6)`

`3/6=1/2,` so we have

`8sqrt(1/2)=(8sqrt(1))/sqrt(2)=8/sqrt(2)`

Answer 2

`4 sqrt2`

Explanation:

`(8 sqrt3)/sqrt6`

Rationalize Denominator

`(8 sqrt3sqrt6)/6`

Combine Roots

`(8 sqrt18)/6`

Factor

`(8 sqrt(9 * 2))/6`

Take Out The Nine

`(8 * 3 sqrt2)/6`

Simplify

`(24 sqrt2)/6`

Simplify

`4 sqrt2`

Answer 3

`(8 sqrt(3))/(sqrt(6)) = 4 sqrt2`

Explanation:

Given:

`(8 sqrt(3))/(sqrt(6))`

Rationalize the denominator:

`rArr (8 sqrt(3))/(sqrt(6))*(sqrt(6))/(sqrt(6))`

`rArr [8 sqrt(3) sqrt(6)]/(sqrt(6) sqrt(6)`

Observe that `color(blue)(sqrt(m) * sqrt(m)=m` and

`rArr color(blue)(sqrt(mn)=sqrt(m)*sqrt(n)`

`rArr [8 sqrt(3) sqrt(3*2)]/6`

`rArr (2*4 sqrt(3) sqrt(3) sqrt(2)]/(2*3)`

`rArr [2*4*3*sqrt(2)]/(2*3)`

`rArr [cancel (2)*4*cancel 3*sqrt(2)]/(cancel(2)*cancel 3)`

`rArr 4 sqrt(2)`

Hence,

`color(red)((8 sqrt(3))/(sqrt(6)) = 4 sqrt2`