Simplify the expression `(4sqrt3)/(2sqrt8)`  Give the exact value in simplified form. Rationalize any denominators. 4 times the square root of 3              over 2 times the square root of 8

Expert Answers
durbanville eNotes educator| Certified Educator

To simplify :


First cross cancel and reduce the contents of the square roots to prime bases:

`therefore = (2sqrt3)/(1sqrt 2^3)` 

Now simplify the `sqrt2^3= sqrt(2.2.2)= 2sqrt2`

`therefore = (2sqrt3)/(2sqrt2)`

Now rationalize the denominator by multiplying by `sqrt2/sqrt2 =1` and cross cancel the `2/2`

`therefore = ((1sqrt3)/(1sqrt2)) times sqrt2/sqrt2` 

`therefore = (sqrt3sqrt2)/(sqrt2sqrt2)`

`therefore = (sqrt3sqrt2)/2` `= sqrt6/2`

aruv | Student

you question is





`` Rationalise the denominator


`` `=sqrt(3xx2)/2`