Between what two consecutive integers do #root3(16)# lie?

2 Answers
Oct 13, 2015

Answer:

#2 and 3#

Explanation:

Pressing #root(3)16# into a calculator gives #2,5198#

This decimal value hence lies between the integers #2# and #3#.

That is, #2,3 in ZZ and root(3)16 in [2;3]#

Oct 13, 2015

Answer:

Between #2# and #3#

Explanation:

#2^3 = 8 < 16 < 27 = 3^3#

and #f(x) = x^3# is strictly monotonic increasing, so

#2 = root(3)(2^3) = root(3)(8) < root(3)(16) < root(3)(27) = root(3)(3^3) = 3#