List of top Mathematics Questions on Real Numbers

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:

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

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 \(14 - 2\sqrt{3}\) 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.

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.

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

Let \(S=\left\{a+b\sqrt2:a,b\in Z\right\},T_1=\left\{(-1+\sqrt2)^n:n\in \N\right\},\ \text{and}\ T_2=\left\{(1+\sqrt2)^n:n\in\N\right\}\). Then which of the following statements is (are) TRUE ?

If $[x]^2 - 5[x] + 6 = 0$, where $[x]$ denotes the greatest integer function, then: