Question

How do you rationalize the denominator and simplify `sqrt(3/2)`?

Answer 1

I got as far as this:

Explanation:

Let us write it as:

`sqrt(3)/sqrt(2)`

multiply and divide by `sqrt(2)`

`sqrt(3)/sqrt(2)color(red)(sqrt(2)/sqrt(2))=(sqrt(3)sqrt(2))/2==sqrt(3*2)/2=sqrt(6)/2`

Answer 2

`sqrt6/2`

Explanation:

`sqrt (3/2)`

`:.=sqrt 3/sqrt 2`

`:.=sqrt 3/sqrt 2xx sqrt 2/sqrt 2`

`:.=sqrt2xxsqrt2=2`

`:.=(sqrt(2xx3))/2`

`:.=sqrt6/2`

Answer 3

`sqrt6/2=1/2sqrt6`

Explanation:

`"using the "color(blue)"laws of radicals"`

`•color(white)(x)sqrt(a/b)hArrsqrta/sqrtb`

`•color(white)(x)sqrtaxxsqrtbhArrsqrt(ab)`

`•color(white)(x)sqrtaxxsqrta=a`

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

`"to eliminate the radical on the denominator multiply"`
`"the numerator/denominator by "sqrt2`

`rArrsqrt3/sqrt2xxsqrt2/sqrt2=(sqrt3xxsqrt2)/(sqrt2xxsqrt2)=sqrt6/2=1/2sqrt6`