Question

How do you rationalize the denominator and simplify `30/sqrt18`?

Answer 1

`5sqrt2`

Explanation:

To rationalise the denominator multiply numerator and denominator by `sqrt18`
`"-------------------------------------------------------"`

Note : `sqrtaxxsqrta = a " eliminate the radical "`

example : `sqrt100xxsqrt100 = 10xx10 = 100`

Also : `sqrtaxxsqrtb hArr sqrtab`
`"-----------------------------------------------------------"`

`rArr 30/sqrt18xxsqrt18/sqrt18=( 30sqrt18)/18 = (5sqrt18)/3`

now `sqrt18 = sqrt(9xx2) = sqrt9xxsqrt2 = 3sqrt2`

hence : `(5sqrt18)/3 = (5xx3sqrt2)/3 = (5cancel(3)sqrt2)/cancel(3)`

`rArr 30/sqrt18 = 5sqrt2`