Question

which integer is closest to (sqrt3{26})?

Explanation:

Step1: Recall cube values

We know that \(2^3 = 8\), \(3^3=27\), and \(4^3 = 64\).

Step2: Compare distances

The value of \(\sqrt[3]{26}\) is between \(2\) and \(3\) (since \(2^3=8<26<27 = 3^3\)). Now, calculate the distance from \(\sqrt[3]{26}\) to \(2\) and to \(3\). The distance from \(\sqrt[3]{26}\) to \(3\) is \(|3-\sqrt[3]{26}|\), and to \(2\) is \(|\sqrt[3]{26}-2|\). Since \(26\) is very close to \(27 = 3^3\), \(\sqrt[3]{26}\) is very close to \(3\) (the difference between \(27\) and \(26\) is \(1\), while the difference between \(26\) and \(8\) is \(18\)). So the integer closest to \(\sqrt[3]{26}\) is \(3\).

Answer:

\(3\)