Between which two consecutive whole numbers is \sqrt[3]{79}Explain your reasoning.

Question

Between which two consecutive whole numbers is
`\sqrt[3]{79}`Explain your reasoning.

Answer 1

Firstly, the expression does not give us an integer result. Since the opposite operation of the cubic root would be power 3, let's try with some easySupe integer numbers:

`\begin{gathered} 2^3=2\cdot2\cdot2=4\cdot2=8 \\ 3^3=3\cdot3\cdot3=9\cdot3=27 \\ 4^3=4\cdot4\cdot4=16\cdot4=64 \\ 5^3=5\cdot5\cdot5=25\cdot5=125 \end{gathered}`

One can see that 79 is between the numbers 64 and 125:

`\begin{gathered} \sqrt[3]{64}<\sqrt[3]{79}<\sqrt[3]{125} \\ 4<\sqrt[3]{79}<5 \end{gathered}`

Therefore, that expression is located between the integer numbers 4 and 5.