Question

What is the sum of the sides of two cubes of volumes 40 cubic inches and 50 cubic inches? Is the sum rational or irrational?

• A. $\sqrt[3]{340}+\sqrt[3]{350}$: Rational
• B. $\sqrt[3]{340}+\sqrt[3]{350}$: Irrational
• C. $\sqrt[3]{340+50}$: Rational
• D. $\sqrt[3]{340+50}$: Irrational

Answer 1

The correct option is B $\sqrt[3]{340}+\sqrt[3]{350}$: Irrational

Square roots of the numbers which are not perfect squares and the cube roots of the numbers which are not perfect cubes are irrational numbers.

Length of Cube 1 = $\sqrt[3]{340}$ inches
Length of Cube 2 = $\sqrt[3]{350}$ inches
Total length = $\sqrt[3]{340}$ + $\sqrt[3]{350}$ inches

Here, 40 and 50 are not the perfect cubes. So, cube roots of both 40 and 50 are irrational numbers.
The sum of two positive irrational numbers is always an irrational number.
So, $\sqrt[3]{340}$ + $\sqrt[3]{350}$ is an irrational number.