Question

which two integers is $sqrt3{26}$ between? 8 and 9 2 and 3 16 and 17 12 and 13

Explanation:

Step1: Recall cube values

We know that for integers, the cube of 2 is \(2^3 = 8\) and the cube of 3 is \(3^3=27\).

Step2: Compare with \(\sqrt[3]{26}\)

We need to find between which two integers \(\sqrt[3]{26}\) lies. Since \(8 = 2^3\) and \(27=3^3\), and \(8<26<27\), taking the cube - root of each part of the inequality (since the cube - root function \(y = \sqrt[3]{x}\) is an increasing function), we get \(\sqrt[3]{8}<\sqrt[3]{26}<\sqrt[3]{27}\), which simplifies to \(2 < \sqrt[3]{26}<3\).

Answer:

2 and 3