Question

1
2.
13
437
999
12
125
Every rational number is
(A) a natural number
(B) an integer
Between two rational numbers
(C) a real number (D) a whole number
(A) There is no rational number (B) there is exactly one rational number (C) there are
infinitely many rational numbers (D) there are only rational numbers and no irrational numbers.
3.
Decimal representation of a rational number cannot be
(A) Terminating
(B) non-terminating (C) non-terminating repeating (D) non terminating
non-repeating
4.
The product of any two irrational numbers is
(A) always an irrational number
(B) always a rational number (C) always an integer
(D) sometimes rational, sometimes irrational
5. The decimal expansion of the number V2 is
(A) a finite decimal (B) 1.41421 (C) non-terminating recurring (D) non-terminating
non-recurring
6. Which of the following is irrational?
(A) 0.14
(B)
0.14 16
(C) 0.1416
(D) 0.4014001400014.......
7.
Are there two irrational numbers whose sum and product both are rationals ? Justify.
8. Find three rational numbers between and
9. Find three rational numbers between - and
10. Express each of the following numbers as a decimal fraction.
ii)
13
iii)
v) kovi) vii) is viii) ? ix)
625
11. Represent the following decimals in the form of repeating decimals as a quotient of integers.
i) 0.2341 ii) 0.052 iii) 15.712 iv) 0.47
v) 0.245 vi) 1.21212121
12. Give an example of each of two different irrational numbers whose:
i) Difference is a rational number ii) sum is a rational number
iii) Product is rational number iv) quotient is rational number.
13. Insert two irrational numbers between i) 2 and 2.5
ii) 0.5 and 0.6 iii) 1 and 2
14. Find the rational numbers a and b, such that
4 +375
V5+ V3
i)
(√2+1)²
ii)
a + b5.
= a + b 15.
= a + b 2.
iii)
√5 - √3
4- 35
√3+3
5 + 2V3
Ξα a-bro v)
atbv3
3V2 - 2V3
7+ 473
√5-1 √5 + 1
+
15. What are the values of a and b if
a + bv5.
√5+1 √5-1
16. Simplify each of the following by rationalising the denominator.
- 3
275 - 15
ii)
iii)
77 + 75
3 V5 - 2V3
3V2
17. Simplify: i)
√6 + √3 √6 + √2
√3-1
773 2/5
372
+
+
√3+1
√10 + √3 √5 + √5 √15+3 √2
3-√2
iv)
473
5 + V
i)
5- VG
V6
VE + V3
2+√3
ii)
2- V3
2- 5
2 + 3​

Answer 1

Answer:

every rational no. is real number