prove √5is an irrational number
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Let us assume that √5 is a rational no.
therefore, √5 = p/q where p and q are integers ; q is not equal to zero
√5 = a/b where a and b are coprimes.
√5b = a
Squaring on both sides
5b²=a²
5b²/a²=1
===>a is a factor of b
let a=10c
5b²/100c²=1
===>c is a factor of b
This proves that b has a factor other than a but we have told that a and b are co primes.
This contradicts that √5 is a rational no.
So we conclude that √5 is an irrational no.
I hope this answer helps you mate!!!
therefore, √5 = p/q where p and q are integers ; q is not equal to zero
√5 = a/b where a and b are coprimes.
√5b = a
Squaring on both sides
5b²=a²
5b²/a²=1
===>a is a factor of b
let a=10c
5b²/100c²=1
===>c is a factor of b
This proves that b has a factor other than a but we have told that a and b are co primes.
This contradicts that √5 is a rational no.
So we conclude that √5 is an irrational no.
I hope this answer helps you mate!!!
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