Question

classify the following root 27 as rational or irrational numbers​

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

Answer:

√27 is rational

Step-by-step explanation:

Let √27 be rational

∴√27=$\frac{a}{b}$ where a and b are co-primes

(√27)²=($\frac{a}{b}$)²

27=$\frac{a^{2}}{b^{2}}$

27b²=a²

∴a² is a factor of 27

∴a is a factor of 27

Let a=27c for some integer c

∴ 27b²=(27c)²

∴b²=27c²

∴b² is a factor of 27

∴b is a factor of 27

This is a contradiction because we had assumed that a and b are co-prime.

∴√27 is irrational