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5. Rationalise the denominators of the following:

(i) \(1\over{\sqrt 7}\)

(ii) \(1\over{\sqrt 7-\sqrt 6}\)  

(iii) \(1\over{\sqrt 5+\sqrt 2}\)

(iv) \(1\over{\sqrt 7-2}\)

Number Systems

Exercise 1.4

Ncert solutions class 9 chapter 1 exercise 4 question 5
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Class 9

Number Systems

Exercise 1.4

1. Classify the following numbers as rational or irrational:

(i) \(2-\sqrt 5\)

(ii) \((3+\sqrt{23})-\sqrt{23}\)

(iii) \({2\sqrt 7}\over{7\sqrt 7}\)

(iv) \(1\over {\sqrt 2}\)

(v) \(2\pi\)

2. Simplify each of the following expressions:

(i) \((3+\sqrt 3)(2+\sqrt 2)\)

(ii) \((3+\sqrt 3)(3-\sqrt 3)\)

(iii) \((\sqrt 5+\sqrt 2)^2\)     

(iv) \((\sqrt 5-\sqrt 2)(\sqrt 5+\sqrt 2)\)

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?

4. Represent \(\sqrt {9.3}\) on the number line.

5. Rationalise the denominators of the following:

(i) \(1\over{\sqrt 7}\)

(ii) \(1\over{\sqrt 7-\sqrt 6}\)  

(iii) \(1\over{\sqrt 5+\sqrt 2}\)

(iv) \(1\over{\sqrt 7-2}\)