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

1 Answer
Jim G.
Mar 21, 2016

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

Related questions
See all questions in Multiplication and Division of Radicals
Impact of this question
1903 views around the world
You can reuse this answer
Creative Commons License