Q1.
Q2.
State whether the following statements are True or False:
(i) Every integer is a rational number.
(ii) Every rational number is an integer.
(iii) Every natural number is a whole number.
(iv) Every whole number is a natural number.
(v) Every whole number is a rational number.
(vi) Every integer is a whole number.
Find three rational numbers between – and − .
Q3.
Give two rational numbers lying between 0.232332333233332 … … .. and
0.212112111211112 … … ….
Q4.
Give two examples of two irrational numbers, the product of which is:
(i) a rational number
(ii) an irrational number
Q5.
Define the following:
(i) Rational numbers
(ii) Irrational numbers
(iii) Real numbers
Q6.
Give five examples of irrational numbers.
Q7.
Identify the following as rational numbers:
√9, √32, √1.69,
, 3.2576, 3.040040004 … . …
Q8.
Find the square root of
Q9.
Simplify 12
Q10. Convert
12
and hence comment on it.
12.
into a decimal.
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Q11. Express (i) 0. 5 (ii) 0.54 in the from
where
and
are integers and
≠ 0.
Q12. Add: 2√2 + 5√3 − 7√5 and 3√3 − √2 + √5
Q13. Simplify:
(i) 4 + √7 3 + √2
(ii) 11 + √11 11 − √11
Q14. Divide: 18√21 by 6√7
Q15. Rationalize the denominator of the following:
(i)
√
(ii)
√
√
Q16. Show by taking examples that the sum of two irrational numbers may
or may not be an irrational number.
Q17. Evaluate: √5 − √3
Q18. Evaluate the following:
(i) √
(ii)
Q19. Simplify:
(i) 7 × 7
(ii) 2 × 3
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Q20. Simplify:
(i)
(ii)
Answers
A1.
(i) True; e.g.−3 =
.
(ii) False; e.g. is not an integer.
(iii) True; e.g. Whole number = 0 and natural numbers
(iv) False; e.g. 0 is not a natural number.
(v) True; e.g. is a rational number.
A2.
(vi) False; e.g.−1 , −2, −3, .. etc are not whole numbers.
− , − , −
0.221, 0.222 are two rational numbers lying between the given rational
numbers.
A4.
(i) √5, √20 (ii) √3, √5
A5. (i) The numbers of the form where and are integers and ≠ 0 are
A3.
known as rational numbers. Example:
, −
(ii) A number is an irrational number, if it has a non- terminating and
non – repeating decimal representation. Example: √7, 1.414215. ..
(iii) All the rational and irrational numbers make up the collection of
real numbers.
A6.√2, √5, , 0.12112111211112. . , √15
A7.
Rational numbers: √9, √1.69, 3.2576
Irrational numbers; √32,
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, 3.040040004
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A8.
√2 = 1.4142135 … … .. It is non –terminating and non –recurring, so it is
an irrational number.
A9. 12
A10. 0.4583
A11. (i) (ii)
A12. √2 + 8√3 − 6√5
A13. (i) 12 + 4√2 + 3√7 + √14
(ii) 110
A14. 3√3
A15. (i) 2 − √3 (ii) 2 − √3
A16. 3 + √5 + 6 − √5 = 9, which is not an irrational number.
√7 − 3 + √2 + 3 = √7 + √2 which is an irrational number.
A17. 8 − 2√15
A18. (i)
(ii)
A19. (i) 7 (ii) (6)
A20. (i) 8
(ii) 3
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