Important questions on Real Numbers

A :-

1. Prove that 4 - 3√2 is an irrational number.
2. Prove that 4 + 4√2 is an irrational number.
3. Prove that 3√2 is an irrational number.
4. Prove that 7√5 is an irrational number.
5. Prove that 6√3 is an irrational number.
6. Prove that 6 - √2 is an irrational number.
7. Prove that √2 is an irrational number.
8. Prove that 2√3 is an irrational number.
9. Prove that √3 is an irrational number.
10. Prove that √5 is an irrational number.

B :-

(Formula related questions)

1. The HCF of two numbers 'a' and 'b' is 5 and their LCM is 200. Then the product of a & b is?
2. If LCM of 20, 25 is 100, then the value of HCF?
3. Given the HCF (99, 153) = 9, then LCM (99, 153) will be?
4. HCF of numbers 96 & 404 is 4. Value of their LCM will be?
5. If LCM (35, 63) = 315 then HCF (35, 63) = ?
6. LCM & HCF of two numbers are 168 & 6 respectively. If one number is 24, then the second number will be?
7. HCF of 15 & 25 is 5, find the L.C.M.?
8. Given that LCM of (132, 288) = 3168 then HCF of (132, 288) will be?
9. If LCM of 26, 156 is 156, then the value of HCF?
10. Formula of H.C.F × L.C.M = I number × II number