Class - 10 Real Numbers Important Questions

Write the HCF of the smallest composite number and the smallest prime number.
Using prime factorization, find HCF and LCM of 96 and 120.
Explain whether (3 × 5 × 13 × 46) + 23 is prime or composite number.
The HCF of two numbers a and b is 5 and their LCM is 200. Find the Product of ab.
Two positive integers a and b can be written as a = x³y² and b = xy³. If x and y are the prime numbers, then find the LCM of (a, b).
Prove that √2 is an irrational number.
Prove that 3 – 2√5 is an irrational number, given that √5 is an irrational number.
If HCF (253, 440) = 11 and LCM (253, 440) = 253 × R, Find the value of R.
Explain, why (7 × 11 × 13) + 13 and (7 × 6 × 5 × 4 × 3 × 2 × 1) + 5 are composite numbers?
The length, breadth and height of a room are 8m 25cm, 6m 75cm and 4m 50cm, respectively. Find the length of the longest rod that can measure the three dimensions of the room exactly.

Class – 10 Real Numbers Important Questions