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

Oct 13, 2015

$2 \mathmr{and} 3$

#### Explanation:

Pressing $\sqrt[3]{16}$ 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

Between $2$ and $3$

#### Explanation:

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

and $f \left(x\right) = {x}^{3}$ is strictly monotonic increasing, so

$2 = \sqrt[3]{{2}^{3}} = \sqrt[3]{8} < \sqrt[3]{16} < \sqrt[3]{27} = \sqrt[3]{{3}^{3}} = 3$