Question

root 7 prove that is irrational

Answer 1

Let root 7 be a rational no
Therefore root 7 =a/b
Thrfr root 7 X b =a
Squaring both sides
49 bXb =aXa
Thrfr it is a factor of aXa
Thrfr it a factor of a
Let a=7c
=>7c=b
=>7 is a factor of b
We proved that 7 is a factor of both a and b
But it cintradicts
=>root 7 is an irrational no

Answer 2

root 7=2.6457513111...and this no. is irrational..


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