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

Question

4062 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-10-13T18:54:55

$2 and 3$

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

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

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

Answer 2 · 2015-10-13T19:13:30

Between $2$ and $3$

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

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

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

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