# RATIONAL AND IRRATIONAL NUMBERS WORKSHEETS I.C.S.E

1. Arrange in ascending order, after inserting three
rational number between 13/6 and 9/7 .
2. Insert five rational numbers between -0.75 and √5.
3. Prove 2/√3 is an irrational number.
4. (a) Prove 6+5√3 is an irrational number.
(b) Prove √5 is an irrational number. Hence show that
2+7√5 is irrational number as well.
5. Prove √x+y is an irrational number.
6. Show that the following are terminating decimal and
rational number –
(a) 0.096
(b) 28.5689
(c) 8.992688
7. Show that the following repeating decimals are rational
number –
(a) 0.8565656…
(b) 1.56708708708…
8. Find the decimal expansion of real number –
(a) 16/13
(b) 21/11
(c) 7/13
9. Locate √7 on a number line.
10. Express 2.62222.. – 0.16666 in p/q form.
11. Without performing actual division, determine
whether the number have a terminating decimal
expansion or a non-terminating repeating expansion –
(a) 19/50
(b) 80/1250
(c) 77/555
12. Write the decimal expansion of the following
number which have termination decimal expansion –
(a) 25/400
(b) 1615/(23 x 52)
(c) 31/243
13. State the reason which of the following are surds
and which are not –
(a) √55
(b) √40 x √65
14. Simply the following –
(a) (2√3 + 7√6) (7 + 2√3)
(b) (7√6 + 3) (7√6 – 3)
15. If x and y are irrational number and (5+2√3)/(7+4√3)
= x-y√3
find the value of x and y.

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