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

1 Answer
Mar 21, 2016

Answer:

#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 #