Question

prove that root 6 is irrational

Answer 1

compare root 6 as rational number and have equal to a/b where a and b are co prime number
now root6 *b=a
taking squre both sides
36b^2=6b
36/6=b^2
6=b^2

Answer 2

Hey mate!

Hete is yr answer.....


Let us assume √6 is rational....


√6 = a/b (a, b are co-primes)

b√6 = a

by squaring on both sides.....


6b² = a²

a² = 6b²

Here, 6 divides a²

Therefore, 6 also divides a ----------(1)

Let a = 6c

By sub. a = 6c in a² = 6b²

(6c)² = 6b²

36c² = 6b²

6c² = b²

b² = 6c²

Here, 6 divides b²

Therefore, 6 also divides b -----------(2)


From (1) & (2)

we can conclude that a, b are not co-primes...

So, our assumption is false.

Hence, √6 is irrational...


Hope it helps...

#BeBrainly...