# 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

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To simplify :

`(4sqrt3)/(2sqrt8)`

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`

**Sources:**

you question is

`(4sqrt(3))/(2sqrt(8))`

`=(4sqrt(3))/(2sqrt(2xx2xx2))`

`=(4sqrt(3))/(2xx2sqrt(2))`

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

`` Rationalise the denominator

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

`` `=sqrt(3xx2)/2`

`=sqrt(6)/2`