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Chapter 1
Q1. Represent
on the number line.
Q2. Represent
on the number line.
Q3. Find the rational number between -2 and 6.
Q4. Find a rational number between
.
Q5. Find three rational numbers between -2 and 5.
Q6. Insert 10 rational numbers between
.
Q7. Insert 100 rational numbers between
Q8. Convert
.
into decimal form by long division method.
Q9.find the decimal representation of
Q10. Express
as a decimal fraction.
Q11.find the decimal representation of
.
Q12. Find the decimal expansion of
Q13. What can the maximum number of digit be in in the repeating block of digits in the
decimal expansion of
Perform the division to check your answer.
Q14. Find the decimal representation of
.
Q15. Express each of the following decimals in the form
i)
ii)
iii)
iv)
v)
vi)
0. ̅
0. ̅
0. ̅
0. ̅
0. ̅
0. ̅
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Q16. Express each of the following decimals in the form
i)
ii)
0.̅̅̅̅
0.̅̅̅̅̅
Q17. Show that 1.272727=1.̅̅̅̅ can be expressed in the form
Q18. Express 0.99999.. in the form
Q19. Express 0.̅̅̅̅̅ as a fraction in the simplest form.
Q20. Convert the following decimal number in the form
i)
ii)
Q21. If
̅
̅̅̅̅
̅̅̅̅̅̅̅̅̅̅̅ write the decimal expression of
without actually doing
the long division.
Q22. Express the following decimals in the form
i)
ii)
iii)
̅̅̅̅
̅
̅̅̅̅
Q23. Express each of the following mixed recurring decimals in the form
i)
ii)
̅
Q24. Show that
̅̅̅̅
̅̅̅̅ can be expressed in the form of
where
Q25. Prove that √ is not a rational number.
Q26. Prove that √ is an irrational number.
Q27. Prove that √ is not a rational number, if
is not a perfect square.
Q28. Give example of two irrational numbers, the product of which is:
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i)
ii)
a rational number
an irrational number.
Q29. Identify √
as rational number or irrational number.
Q30. Insert a rational and an irrational number between 2 and 3.
Q31. Find two irrational number between 2 and 2.5.
Q32. Find two irrational numbers lying between √
√
Q33. Find two irrational number between 0.12 and 0.13.
Q34. Find two rational number between 0.23332333233332…. and 0.2525525552555…
Q35. Find a rational number and also an irrational number between the numbers a and b given
below:
a = 0.101001000100001…
b= 0.1001000100001…..
Q35. Find one irrational number between the number a and b given below.
a = 0.1111…. b=0.1101
Q36. Find three different irrational numbers between the rational numbers
.
Q37. Write three numbers whose decimal expansion are non-terminating non-recurring.
Q38. Prove that √ - √ is an irrational number.
Q39. Examine , whether the following numbers are rational or irrational.
i)
(√
ii)
(
iii)
)
√ )(
√ )
√
Q40. Show how √ can be represented on the number line.
Q41. Represent √
on the number line.
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Part II
Q1. Evaluate each of the following:
i)
ii)
iii)
(
iv)
( )
v)
( )
)
Q2. Evaluate each of the following:
i)
( )
( )
( )
ii)
( )
( )
( )
( )
( )
( )
iii)
iv)
Q3. If
then find the value of each of the following:
i)
ii)
iii)
iv)
( )
v)
(
)
Q4. Evaluate each of the following removing radical signs and negative indices wherever they
occur:
i)
ii)
iii)
(
(
(
)
iv)
( )
)
)
Q5. Simplify each of the following , removing radical signs and negative indices wherever they
occur:
i)
(√ )
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(√ ) (√ )
ii)
iii)
√
iv)
(
)
v)
(√ )
vi)
(√ ) (√ )
√
Q6. Simplify each of the following:
i)
(
)
ii)
(
)
iii)
(
)
iv)
√(
)
Q7. Assuming that
i)
√
ii)
(
iii)
(√
iv)
(√ )
v)
√
vi)
√√
are positive real numbers, simplify each of the following:
)
)
√
√
Q8. Simplify :
(
i)
)
(
(
)
)
( )
ii)
Q9. Simplify : ( )
Q10. If
√
[( )
( ) ]
are positive real numbers show that:
√
√
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Q11. Show that:
i)
ii)
(
)
(
)
(
( )
) (
) (
(
)
(
Q12. If
)
(
)
)
Q13. Prove that :
Q14. Find the value of
Part III
Q1. Simplify each of the following:
i)
ii)
√
√
√
√
Q2. Simplify the following expressions:
i)
(
√ )(
√ )
ii)
(
√ )(
√ )
√ )(
√ )
Q3. Simplify:
i)
(
ii)
(
√ )(
√ )
Q4. Simplify:
i)
(√
ii)
(√
√ )
√ )
Q5. Rationalise the denominator of
√
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Q6. Rationalise the denominator of
Q7. Rationalise the denominator of
√
√
Q8. Rationalise the denominator of
√
√
Q9. Rationalise the denominator in each of the following:
i)
ii)
iii)
√
√
√
√
Q10. Given that √
approximately, find to three places of decimals the value of
√
Q11. Find the value to three places of decimals, of each of the following: it is given that
√
√
i)
ii)
iii)
√
√
(
)
√
√
√
Q12. Find the value to three places of decimals, of each of the following: it is given that
√
√
i)
ii)
iii)
√
√
(
)
√
√
√
√
√
√
√
Q13. If √
find the value of √
√ up to three places of decimals.
Q14. Simplify each of the following by rationalising the denominator:
i)
ii)
iii)
√
√
√
√
√
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iv)
√
√
√
√
Q15. If both a and b are rational numbers, find the values of a and b in each of the following
equalities:
i)
√
√
ii)
√
√
√
iv)
vi)
√
√
√
iii)
v)
√
√
√
√
√
√
√
√ √
√ √
√
√
√
Q16. Simplify each of the following:
i)
ii)
iii)
√
√
√
√
√
√
√
√
√
√
Q17. Show that
√
Q18. Prove that :
√
√
√
√
√
√
√
(
√
Q21. If
Q24. If
√
√
√
√
√
√
√
√
√
√
√
√
√
Q20. . If
Q23. If
√
√
√
Q19. If
Q22. If
√
√
√
√
√
√
√
√
√
√
√
√
√
)
√
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Q25. Evaluate
√
√
√
√
√
is being given that √
√
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