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Q.1. What is the value of (2^{3})^{2}?
Solution.
(2^{3})^{2} = 2^{3x2} [∵ (x^{m})^{n} = x^{m.n}]
= 2^{6} =2 x 2 x 2 x 2 x 2 x 2 = 64
Q.2. What is the value of (625) ^{1/4 }?
Solution.
Q.3. Which of the following are irrational numbers?
√3, √4, √5, 22/7, π, 0
Solution. √3, √5 and π are irrational numbers.
Q.4. Which of the following are rational?
2√3, 1, 0, 3.14, π, 22/7
Solution. 1, 0, 3.14 and 22/7 are rational numbers.
Q.5. Which of the following cube roots is not irrational?
3 √5, 3√6, 3√7, 3√8, 3√9
Solution. 3√8 is not an irrational number.
Q.6. Which three integers are equal to their own cube roots?
Solution. –1, 0 and 1
[∵ 3√1 = 1, 3√1 = 1 and 3√0 = 0 ]
Q.7. Is the following number rational or irrational? 0.0769230769230769230...
Solution.
The given number is rational. [∵ “076923” repeats]
Q.8. Is 0.666 ...a “nonterminating rational” or “nonterminating recurring rational number”?
Solution. Nonterminating rational number.
Q.9. Is 1.27 27 27 ... nonterminating recurring or nonterminating nonrecurring number?
Solution. It is a nonterminating recurring rational number.
Q.10. The decimal representation of √3 is 1.73205807... . Is it nonterminating nonrecurring?
Solution. Yes
Q.11. Is the product of a rational and an irrational number, rational?
Solution. No. It is an irrational number.
Q.12. Write the smallest nonnegative integer.
Solution. ‘0’ Question
Q.13. Write the smallest positive integer.
Solution. 1 Question
Q.14. Up to how many decimal places, π and 22/7 are same?
Solution. π and 22/7 are same only up to 2 decimal places.
[∵ 22/7 = 3.142857142... and π =3.141592653589...]
Q.15. Which of the following is irrational?
Solution. √7 is irrational.
Q.16. Which of the following is the value of 0.999... expressed as p/q :
(i) 9/10
(ii) 1
(iii) 999/1000
Solution. 0.999... = 1
Q.17. What is a terminating decimal?
Solution. The number with a finite decimal part is known as terminating decimal.
Example: 0.375 is a terminating decimal.
Note: If we express a rational number as a decimal number and the remainder becomes zero after a certain stage, then the decimal expansion is terminating.
Terminating Decimal
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