Question

Prove the cube root of 13 is irrational.

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

Step-by-step explanation:

Prove that the cube root of 3 is irrational:

∛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.

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