prove that √5 is irrational
Answers
Answered by
0
If possible then let √5 as a rational number .
=> √5 = p/q p & q E z , q is not equal to 0 .
=> √(5)² = p²/q² (squaring both sides)
Multiplying q both sides
=> 5q = p²/q --------- (1)
But,
=> 4<5<9
=> √4 < √5 < √9
=> 2 < √5 < 3
Hence, √5 lies between 2 & 3.
√5 is not equal to Integer.
Therefore,. q is not equal to 0 , is not equal to 1.
Putting p = 1 and q = 2 in equation.
=> 5 x 2 = 1/2
=> 10 = 1/2
Integer = Fraction, which is not possible.
Hence, √5 is an irrational number.
Proved.....
Similar questions