Question

prove that the cube root of 3 is irrational..

Answer 1

Prove that the cube root of 3 is irrational:

In this, we need to prove that ∛3 is a irrational number. so, we need to assume that ∛3 is rational number.

The rational number is written as p/q where p and q are integers. q ≠ 0.

∛3 = p/q → (equation 1)

When equation (1) is cubed, then

3 = p³/q³

∴ 3q³ = p³

p³ is a perfect cube and 3q³ must also be perfect cube.

In 3q³ then q is a perfect cube whereas 4 is not a perfect cube.

Hence, the assumption is wrong. So, ∛3 is cannot be written as p/q.

Thus, ∛3 is a irrational number.

Hence proved.

Answer 2

Answer:

We nned to probe this by contradiction.