List of top Mathematics Questions on Real Numbers

The HCF of 960 and 432 is :

Prove that \(2 + 3\sqrt{5}\) is an irrational number given that \(\sqrt{5}\) is an irrational number.

For any natural number n, \( 5^n \) ends with the digit :

If the product of two numbers is 2880 and their H.C.F. is 12, then the value of their L.C.M. is:

The dimensions of a window are 156 cm \(\times\) 216 cm. Arjun wants to put grill on the window creating complete squares of maximum size. Determine the side length of the square and hence find the number of squares formed.

Prove that $2\sqrt{2}$ is an irrational number.

LCM of the numbers 12 and 20 will be :

HCF of the numbers 49 and 91 will be :

LCM and HCF of two numbers are 182 and 13 respectively. If one number is 26, then other number will be :

A trader has three different types of oils of volume \(870 \text{ l}\), \(812 \text{ l}\) and \(638 \text{ l}\). Find the least number of containers of equal size required to store all the oil without getting mixed.

What do you understand by irrational number? Prove that \( 5 - 3\sqrt{2} \) is an irrational number.

Assertion (A): The number \(4^n\) cannot end with the digit 0, where \(n\) is a natural number.
Reason (R): A number ends with 0 if its prime factorization contains both 2 and 5.

If the product of two numbers is 2880 and their H.C.F. is 12, then the value of their L.C.M. is:

There are two sections A and B of Grade X. There are 28 students in Section A and 30 students in Section B. What is the minimum number of books you will acquire for the class library so that they can be distributed equally among students of Section A or Section B ?

If the HCF of 210 and 55 is expressed as \(210 \times 5 + 55m\), then find the value of \(m\).

Assertion (A) : H.C.F. \((36 m^{2}, 18 m) = 18 m\), where \(m\) is a prime number.
Reason (R) : H.C.F. of two numbers is always less than or equal to the smaller number.

Prove that \(14 - 2\sqrt{3}\) is an irrational number, given that \(\sqrt{3}\) is irrational.

Prove that \( \sqrt{5} \) is an irrational number.

Prove that \(\sqrt{3}\) is an irrational number.

The natural number 2 is :

Prove that \(\sqrt{3}\) is an irrational number.

The HCF of \(2^2 \cdot 3^3\) and \(3^2 \cdot 2^3\) is :

Which of the following numbers will not end with 0 for any natural number \(n\)?

Assertion (A): \(7 \times 2 + 3\) is a composite number.
Reason (R): A composite number has more than two factors.

Given that \(\sqrt{5}\) is an irrational number, prove that \(3 + 2\sqrt{5}\) is also an irrational number.