REAL NUMBERS (X)
1.
If 7x5x3x2 + 3 is composite number? Justify your answer
2. Show that any
positive odd integer is of the form 4q + 1 or 4q +3 where q is a positive
integer
3. Prove that √2
+ √5 is irrational
4. Prove that 5 -
2√3 is an irrational number
5. Prove that √2
is irrational
6. Use Euclid’s
Division Algorithms to find the H.C.F of a) 135 and 225
b) 4052 and 12576
c) 270, 405 and 315
7. Find the HCF
and LCM of 26 and 91 and verify that LCM X HCF = Product of two numbers
8. Explain
why 29 / 23 x 53 is a terminating decimal expansion
9. 163 /150 will have a terminating decimal expansion. State true or false .Justify
your answer.
10. Find HCF of 96 and 404 by prime
factorization method. Hence, find their LCM.
11. Using prime
factorization method find the HCF and LCM of 72, 126 and 168
12. If HCF (6, a)
= 2 and LCM (6, a) = 60 then find a
13. given that
LCM (77, 99) = 693, find the HCF (77, 99)
14. Find the
greatest number which exactly divides 280 and 1245 leaving remainder 4 and
3
15. The LCM of
two numbers is 64699, their HCF is 97 and one of the numbers is 2231. Find the
other
16. Two numbers
are in the ratio 15: 11. If their HCF is 13 and LCM is 2145 then find the
numbers
17. Express
0.363636………… in the form a/b
18. Write the HCF
of smallest composite number and smallest prime number
19. Write
whether 2√45 + 3√20 on simplification give a rational or an
irrational number
2√5
20. State whether
10.064 is rational or not. If rational, express in p/q form
21. Write a
rational number between √2 and √3
22. State the fundamental
theorem of arithmetic 
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