The document Worksheet - Real Numbers Class 10 Notes | EduRev is a part of the Class 10 Course Mathematics (Maths) Class 10.

All you need of Class 10 at this link: Class 10

**1.** Find the H CF of 231 and 396, using Euclidâ€™s division algorithm.

**2.** Can two numbers have 18 as their HCF and 380 as their LCM? Give reason.

**3.** Show that the square of an odd positive integer is of the form 8m + 1, for some wholenumber m.

**Hint: **

For a whole number â€˜qâ€™, we have (2q + 1) any positive integer.

âˆµ (2q + 1)^{2} = 4q^{2} + 4q + 1 = 4q(q + 1) + 1

Since, q(q + 1) is either 0 or even

âˆµ Let it be 2m, where m is a whole number

â‡’ (2q + 1)^{2} = 4[q(q + 1)] + 1

= 4[2m] + 1

= 8m + 1

**4.** Find the largest number which divides 248 and 1032 leaving remainder 8 in each case.

**5.** Given that LCM of two numbers is 1449 and their HCF is 23. If one of the numbers is 207, find the other.

**6.** Find the greatest number of 6-digits which is exactly divisible by 15, 24 and 36.

**7.** Prove tha teach of the following is an irrational.

**8.** Prove that p is not a rational number, if p is not a perfect square.

**9. **Prove that the difference and quotient of are irrational.

**ANSWERS**

1. 33

2. No, [âˆµ the HCF (18) does not divide LCM (380)]

4. 16

5. 161

6. 999720

Offer running on EduRev: __Apply code STAYHOME200__ to get INR 200 off on our premium plan EduRev Infinity!

178 videos|268 docs|103 tests

### Important definitions and formulas - Real Numbers

- Doc | 1 pages
### Fundamental Theorem of Arithmetic

- Video | 15:20 min
### Hots Questions - Real Numbers

- Doc | 1 pages
### NCERT Textbook - Real Numbers

- Doc | 19 pages
### NCERT Exemplar - Real Numbers

- Doc | 3 pages
### Ex 1.1 NCERT Solutions - Real Numbers

- Doc | 5 pages

- Facts that Matter- Real Numbers
- Doc | 1 pages
- Previous Year Questions - Real Numbers
- Doc | 6 pages