show that 5root6 is an irrational number
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root 5 is shown as irraratinal
let us Hume that root 5 is irrational number it can be expressed in the form of a/b where A and B are positive integers and B not equal to zero.
root 6 =a/b
squaring on both sides
6 = a square
6 b square = a square. equa.1
therefore 6 decimal square it follows that 6 divide a
a = 6c and put this value in a question first
6b square = 6c square
25/5c = b square
5c square = b square --- equa. 2
it means b square is divisible by 6 follows that B is divisible by 6
from equation first and second
we say that 6 is a common factor of both A and B but this contradicts the fact that A and B are co-prime .
they have no common factor
so our assumption that root 6 is a rational number is wrong
therefore root 5 is an irrational number
let us Hume that root 5 is irrational number it can be expressed in the form of a/b where A and B are positive integers and B not equal to zero.
root 6 =a/b
squaring on both sides
6 = a square
6 b square = a square. equa.1
therefore 6 decimal square it follows that 6 divide a
a = 6c and put this value in a question first
6b square = 6c square
25/5c = b square
5c square = b square --- equa. 2
it means b square is divisible by 6 follows that B is divisible by 6
from equation first and second
we say that 6 is a common factor of both A and B but this contradicts the fact that A and B are co-prime .
they have no common factor
so our assumption that root 6 is a rational number is wrong
therefore root 5 is an irrational number
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