Which of the following numbers is rational?
\(\sqrt[3]{1331}\)
\(\sqrt[3]{1331}\) is correct.
A number is called rational if it can be written as a ratio of two integers; equivalently, a root of a natural number is rational only when that natural number is a perfect power of the required order.
Step 1 — Check each option. 1221 is not a perfect square (\(34^{2} = 1156\), \(35^{2} = 1225\)), so \(\sqrt{1221}\) is irrational. 1441 is not a perfect fourth power, and 1551 is not a perfect fifth power.
Step 2 — 1331 is a perfect cube because \(11^{3} = 11 \times 11 \times 11 = 1331\), so \(\sqrt[3]{1331} = 11\), an integer and therefore rational.
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