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

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Answer 1 · 2015-10-09T02:23:17

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

Factor 16, down to its primes

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#