Question

Which of the following is an irrational number? (A) $2.3$, (B) $\sqrt{13} \times \sqrt{13}$, (C) $\sqrt{441}$

Hint:

Quick checks:
Terminating decimals → rational
$\sqrt{a} \times \sqrt{a} = a$
Square root of perfect square → rational
Only roots of non-perfect squares are irrational.

Answer 1

Concept:
Rational numbers can be written in the form \( \frac{p}{q} \).
Irrational numbers cannot be written as fractions.
The square root of a perfect square is rational.
Option (A): 2.3
\[ 2.3 = \frac{23}{10} \] This is a fraction, so it is rational.
Option (B): \( \sqrt{13} \times \sqrt{13} \)
\[ \sqrt{13} \times \sqrt{13} = 13 \] Since 13 is an integer, it is rational.
Option (C): \( \sqrt{441} \)
\[ 441 = 21^2 \] \[ \sqrt{441} = 21 \] This is also rational.
Conclusion:
All given options are rational numbers. Hence, none of them is irrational.
\[ \boxed{\text{None of these}} \]