How do you simplify #root3(16 )+ 3+root3(54))#?

1 Answer
Oct 9, 2015

Answer:

#5root(3)(2) + 3#

Explanation:

Factor 16, down to its primes

#16|2#
#color(white)(0)8|2#
#color(white)(0)4|2#
#color(white)(0)2|2#
#color(white)(0)1| 2^4#

Factor 54, down to its primes

#54|2#
#27|3#
#color(white)(0)9|3#
#color(white)(0)3|3#
#color(white)(0)1|2*3^3#

Subsitute these

#root(3)(2^3*2) + 3 + root(3)(2*3^3)#

Everything with an exponent that's 3 or a multiple of it can come out of the root

#2root(3)(2) + 3 + 3root(3)(2)#

Sum everything that has #root(3)(2)# together

#5root(3)(2) + 3#