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Simplify the expression `(4sqrt3)/(2sqrt8)`  Give the exact value in simplified form....

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schooledmom | Salutatorian

Posted June 12, 2013 at 12:58 PM via web

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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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aruv | High School Teacher | Valedictorian

Posted June 12, 2013 at 1:13 PM (Answer #1)

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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`

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durbanville | High School Teacher | (Level 1) Educator Emeritus

Posted June 12, 2013 at 1:48 PM (Answer #2)

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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`

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