Irrational Numbers on a Number Line

Since each irrational number can be represented as infinite decimal, then we can proceed in the same way, as we did when placed decimals on a number line.

$$$\pi\approx{3.14}$$$, so it is slightly to the right of 3.

Since $$${4}<{5}<{9}$$$, then $$$\sqrt{{{4}}}<\sqrt{{{5}}}<\sqrt{{{9}}}$$$ or $$${2}<\sqrt{{{5}}}<{3}$$$. So, $$$\sqrt{{{5}}}$$$ is somewhere between 2 and 3 (close to 2, because $$$\sqrt{{{5}}}\approx{2.236}$$$).

Similarly, since $$$-{64}<-{50}<-{27}$$$, then $$${\sqrt[{{3}}]{{-{64}}}}<{\sqrt[{{3}}]{{-{50}}}}<{\sqrt[{{3}}]{{-{27}}}}$$$ or $$$-{4}<\sqrt{{-{50}}}<-{3}$$$. So, $$${\sqrt[{{3}}]{{-{50}}}}$$$ is somewhere between -4 and -3 (closer to -4, because $$${\sqrt[{{3}}]{{-{50}}}}\approx-{3.684}$$$).