How do you rationalize the denominator and simplify #sqrt (1 / 3)#?

1 Answer
Apr 9, 2018

Answer:

#(sqrt3)/3#

Explanation:

law of surds:

#(sqrta)/(sqrtb) = sqrt(a/b)#

here, #sqrt(a/b) = sqrt(1/3)#.

using this law, #sqrt(1/3)# is the same as #(sqrt1)/(sqrt3)#.

#sqrt1# is #1#, so #sqrt(1/3)# is the same as #1/(sqrt3)#.

the denominator can be rationalised by multiplying both the numerator and the denominator by #sqrt3#.

#1 * sqrt3 = sqrt3#

#sqrt3 * sqrt3 = 3#

#1/(sqrt3) = (1 * sqrt3)/(sqrt3 * sqrt3)#

#= (sqrt3)/3#