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})· 

3. Recall, π is defined as the ratio of the circumference (say c) of a circle to its diameter (say d). That is, (pi={cover d})·  This seems to contradict the fact that π is irrational. How will you resolve this contradiction?

Number Systems

Exercise 1.4

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

(iv) (1over {sqrt 2})

(v) (2pi)

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={cover 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) (1over{sqrt 7})

(ii) (1over{sqrt 7-sqrt 6})  

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

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

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