The number \( \sqrt{21} \) is actually irrational. A rational number can be expressed as the ratio of two integers (a fraction), while an irrational number cannot be expressed in this way.
The reason \( \sqrt{21} \) is considered irrational is that 21 is not a perfect square. The square roots of perfect squares (such as 1, 4, 9, 16, etc.) result in whole numbers, while the square root of 21 does not simplify to a whole number or a simple fraction.
To confirm, there are no two integers \( a \) and \( b \) such that \( \left(\frac{a}{b}\right)^2 = 21 \). Since 21 is not a perfect square, \( \sqrt{21} \) is irrational.