**Real Numbers**

**1. Insert 4 rational numbers between 1 and without using formula **

** Sol: we have to insert 4 rational numbers between 1 and and 1**

** 4 +1 = 5 **

**1 can be written as **

**Lcm of (4, 5) = 20**

**2. The prime factorisation of a natural number (n) is 2 ^{3} × 3^{2} × 5^{2} × 7. How many consecutive zeros will it have at the end of it? Justify your answer.**

**Sol: **

** n = 2 ^{3} × 3^{2} × 5^{2} × 7 **

** = 2 × 2 ^{2} × 3^{2} × 5^{2} × 7 **

** = 2 × 3 ^{2} × 7 (5^{2} × 2^{2}) **

** = 2 × 3 ^{2} × 7 × (10)^{2} = 12600**

**∴ n has 2 consecutive zeros at the end**

**3. Find the value of **

**Sol:**

**4. Write any two irrational numbers between 3 and 4**

**Sol: **

** **

** 5. Find the value of **

** **

** 6. Find the HCF and LCM of 90, 144 by using the prime factorisation method**

**Sol:**

**7. Is rational or irrational? justify your answer**

**Sol:**

**8. Expand **

**Sol:**

**9. Find the HCF of 24 and 33 by using division method**

**Sol:**

**33 > 24**

** 33 = 24 × 1 + 9**

** 24 = 9 × 2 + 6**

** 9 = 6 × 1 + 3**

** 6 = 3 × 2 + 0**

**∴ HCF of 24 ****and 33 = 3**

**10. Find the value of **

**Sol:**

**11. Ramu says, “if = 0, the value of x is 0”. Do you agree with him? Give reason.**

**Sol:**

**1. Write any three numbers of two digits. Find the LCM and HCF for the above numbers by the prime factorisation method.**

**Sol: let 10, 12, 16 be three two-digit numbers**

** Prime factarisation of 10 = 2 × 5 = 2 ^{1}× 5^{1}**

** Prime factarisation of 12 = 2 × 2× 3 = 2 ^{2} × 3**

** Prime factarisation of 16 = 2 × 2× 2× 2 = 2 ^{4}**

**HCF of 10, 12 and 16 = 2 ^{1} = 2**

**LCM of 10, 12 and 16 = 2 ^{4} × 3× 5 = 8 × 3× 5 = 120**

**2. Give an example for each of the following**

**(i) The product of two irrational numbers is a rational number**

**(ii) The product of two irrational numbers is an irrational number**

**Sol:**

**3. State with reasons which of the following are rational numbers and which are irrational numbers**

** **

**4. Expand **

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