CLASS: IX
NUMBER SYSTEM
1. Find three irrational numbers between 2 and 3.
2. Find five rational numbers between -1 and 1.
3. Convert each of the following into a decimal:
(I)
(II)
(III)
(I)
4. Express each of the following in the form of
.
(i) 0. ̇ (ii) 4.8 ̇ ̇ (iii) 1. ̇ 4 ̇
5. Represent the following numbers on the number line:
(i) √ (i) √ (i) √ (i) √
6. Represent the following numbers on the number line:
(i) √
(i) √
(i) √
(i) √
7. Rationalise the denominator of the following numbers:
(i)
√
(ii)
(iii )
–√
√
(iv)
√
(v)
√ –
√ –
√
–√
(vi)
√
√
√
(vii)
√
√ – √
8. Find the values of ‘a’ and ‘b’ if,
(i)
√
= a + b√
(ii)
√
= a + b√
(iii)
– √
= a + b√
√
9. Simplify:
(i)
–√
√
+
√
–√
(ii)
√
–√
+
–√
√
(iii)
√ – √
√
√
+
√
√
√
√
(iv)
√
√
–
– √
–√
10. Rationalise the denominator of the following:
(i)
–√
√
(ii)
√
√ –√
11. Rationalise the denominator of
12. If x =
– √
and y =
√
√
(iii)
√
√
√
√
√ –√
–√
√
√
.
, find the values of x2 + y2.
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