Question
Which of the following is irrational?
(a) \( \sqrt{\frac{4}{9}} \)
(b) \( \frac{4}{5} \)
(c) \( \sqrt{7} \)
(d) \( \sqrt{81} \)
Solution
Option (a): \( \sqrt{\frac{4}{9}} \)
\[ \sqrt{\frac{4}{9}} = \frac{2}{3} \]
✔ Rational
Option (b): \( \frac{4}{5} \)
✔ Rational
It is already in fraction form.
Option (c): \( \sqrt{7} \)
✔ Irrational
7 is not a perfect square, so \( \sqrt{7} \) is irrational.
Option (d): \( \sqrt{81} \)
\[ \sqrt{81} = 9 \]
✔ Rational
Final Answer
✔ Correct option: (c) \( \sqrt{7} \)