List of top Mathematics Questions on Real Numbers

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 ?

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

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

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.

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.

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.

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

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

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

The HCF of 960 and 432 is :

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.

The HCF of 960 and 432 is :

The natural number 2 is :

Assertion (A) : \((a + \sqrt{b})(a - \sqrt{b})\) is a rational number, where a and b are positive integers.
Reason (R) : Product of two irrationals is always rational.

Prove that \(5 - \sqrt{3}\) is an irrational number.

Using Euclid's division algorithm, find the H.C.F. of 504 and 1188.

In division algorithm a=bq+r, b=4, q=5 and r=1, then what is the value of a?

Which of the following fractions has terminating decimal expansion?

In the form of \(\frac{p}{2^n \times 5^m}\), 0.505 can be written as