3. Recall, π is defined as the ratio of the circumference (say c) of a circle to its diameter (say d). That is, \(\pi={c\over d}\)· This seems to contradict the fact that π is irrational. How will you resolve this contradiction?
Class 9
Number Systems
Exercise 1.4
1. Classify the following numbers as rational or irrational:
(ii) \((3+\sqrt{23})-\sqrt{23}\)
(iii) \({2\sqrt 7}\over{7\sqrt 7}\)
2. Simplify each of the following expressions:
(i) \((3+\sqrt 3)(2+\sqrt 2)\)
(ii) \((3+\sqrt 3)(3-\sqrt 3)\)
(iv) \((\sqrt 5-\sqrt 2)(\sqrt 5+\sqrt 2)\)
4. Represent \(\sqrt {9.3}\) on the number line.
5. Rationalise the denominators of the following:
(ii) \(1\over{\sqrt 7-\sqrt 6}\)