Read and download free pdf of CBSE Class 10 Mathematics Real Numbers Worksheet Set D. Students and teachers of Class 10 Real Numbers can get free printable Worksheets for Class 10 Real Numbers in PDF format prepared as per the latest syllabus and examination pattern in your schools. Standard 10 students should practice questions and answers given here for Real Numbers in Grade 10 which will help them to improve your knowledge of all important chapters and its topics. Students should also download free pdf of Class 10 Real Numbers Worksheets prepared by school teachers as per the latest NCERT, CBSE, KVS books and syllabus issued this academic year and solve important problems provided here with solutions on daily basis to get more score in school exams and tests

## Real Numbers Worksheet for Class 10

Class 10 Real Numbers students should refer to the following printable worksheet in Pdf in standard 10. This test paper with questions and answers for Grade 10 Real Numbers will be very useful for exams and help you to score good marks

### Class 10 Real Numbers Worksheet Pdf

**Real Numbers**

**Q.- Insert a rational and an irrational number between 2 and 3.**

**Sol.**If a and b are two positive rational numbers such that ab is not a perfect square of a rational number, then √ab is an irrational number lying between a and b. Also, if a,b are

**Q.-**

**Prove that**

**(i) √2 is irrational number**

**(ii) √3 is irrational number**

**Similarly √5, √7, √11…... are irrational numbers.**

**Sol.**(i) Let us assume, to the contrary, that 2 is rational.

^{2}= a

^{2}. Therefore, 2 divides a

^{2}. Now, by

^{2}= 4c

^{2}, that is,

^{2}= 2c

^{2}.

^{2}, and so 2 divides b (again using Theorem with p = 2).

^{2}= a

^{2}.

^{2}is divisible by 3, and by Theorem, it follows that a is also divisible by 3.

^{2}= 9c

^{2}, that is,b

^{2}= 3c

^{2}.

^{2}is divisible by 3, and so b is

**Q.-**

**Using Euclid’s division algorithm, find the**

**H.C.F. of [NCERT]**

**(i) 135 and 225**

**(ii) 196 and 38220**

**(iii) 867 and 255**

**Sol.**(i) Starting with the larger number i.e., 225, we get:

**(Ans.)**

**(Ans.)**

**Q.-**

**Show that one and only one out of n; n + 2 or n + 4 is divisible by 3, where n is any positive integer.**

**Sol.**Consider any two positive integers a and b such that a is greater than b, then according to Euclid’s division algorithm:

**=> n + 2 is divisible by 3**

**=> n + 4 is divisible by 3**

**Hence the required result.**

**Q.-**

**Consider the number 6n, where n is a natural number. Check whether there is any value of**

**n ϵ N for which 6n is divisible by 7.**

**Sol.**Since, 6 = 2 × 3; 6n = 2n × 3n

**(Ans)**

**More question-**

1. If 7 x 5 x 3 x 2 + 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. Show that 8n cannot end with the digit zero for any natural number n

4. Prove that 3√2 is irrational 5

5. Prove that √2 + √5 is irrational

6. Prove that 5 – 2 √3 is an irrational number

7. Prove that √2 is irrational

8. Use Euclid’s Division Algorithms to find the H.C.F of a) 135 and 225 (45)

b) 4052 and 12576 (4)

c) 270, 405 and 315 (45)

9. Using Euclid’s division algorithm, check whether the pair of numbers 50 and 20 are co-prime or not.

10. Find the HCF and LCM of 26 and 91 and verify that LCM X HCF = Product of two numbers (13,182)

11. Explain why 29 is a terminating decimal expansion 23 x 53

12. 163 will have a terminating decimal expansion. State true or false .Justify your answer. 150

13. Find HCF of 96 and 404 by prime factorization method. Hence, find their LCM. (4, 9696)

14. Using prime factorization method find the HCF and LCM of 72, 126 and 168 (6, 504)

15. If HCF (6, a) = 2 and LCM (6, a) = 60 then find a (20)

16. given that LCM (77, 99) = 693, find the HCF (77, 99) (11)

17. Find the greatest number which exactly divides 280 and 1245 leaving remainder 4 and 3 (138)

18. The LCM of two numbers is 64699, their HCF is 97 and one of the numbers is 2231. Find the other (2813)

19. Two numbers are in the ratio 15: 11. If their HCF is 13 and LCM is 2145 then find the numbers (195,143)

20. Express 0.363636………… in the form a/b (4/11)

21. Write the HCF of smallest composite number and smallest prime number

22. Write whether 2√45 + 3√20 on simplification give a rational or an irrational number 2√5 (6)

23. State whether 10.064 is rational or not. If rational, express in p/q form

24. Write a rational number between √2 and √3

25. State the fundamental theorem of arithmetic

26. The decimal expansion of the rational number 74 will terminate after ………. Places

23 . 54

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