Question

Root 6 is irrational prove that

Answer 1

Answer:

Explanation:

Let us assume that √6 is an irrational number which can be represented in the form a/b where a and b are co-prime numbers and b≠0.

√6 = $\frac{a}{b}$

[ Squaring both sides}

6 = a²/b²

6b² = a²

[ 6 is divisible by a², so it is also divisible by a]

Let a = 6c

6b² = (6c)²

6b² = 36c²

b² = 6c²

[ 6 is divisible by b², so it is also divisible by c]

It is given that a and b are co-primes, but both a and b are 6 as their common factor other than 1.

This tells us that they are not co-prime. This contradicts our assumption that a and b are co-primes.

Hence it is proved that √6 is irrational.