Question

Which of the following is always rational?

• A. The hypotenuse of a right angled isosceles triangle with side which is rational.
• B. The area of a square, given the side is irrational
• C. The volume of a cube given side is rational
• D. The area of rectangle in which one of the sides is irrational.

Answer 1

The correct option is C

The volume of a cube given side is rational

Let the side of the triangle be $a$. By Pythagoras theorem hypotenuse = $\sqrt{a^2+a^2}=\sqrt{2}a$

The square of an irrational number can be either rational or irrational. So, the area can be rational or irrational

Volume = $a^3$ Cube of a rational number is always rational.

Product of non-zero rational and irrational is always irrational.