Math, asked by dinedk, 11 months ago

prove that √5 is irrational​

Answers

Answered by aaravshrivastwa
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.....

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