Question

Prove that √5 is irrational ​

Answer 1

Let us assume that √5 is a rational number.

we know that the rational numbers are in the form of p/q form where p,q are intezers.

so, √5 = p/q

     p = √5q

we know that 'p' is a rational number. so √5 q must be rational since it equals to p

but it doesnt occurs with √5 since its not an intezer

therefore, p =/= √5q

this contradicts the fact that √5 is an irrational number

hence our assumption is wrong and √5 is an irrational number.

HOPE IT WILL HELP U.....

Answer 2

Answer:

Step-by-step explanation:

let us assume that √5 be rational

Then it must in the form of p/q [q is not equal to 0][p and q are co-prime]

√5=p/q

=> √5 ×q = p

squaring on both sides

=> 25q² = p²  ------> 1

p² is divisible by 5

⇒p is divisible by 5

Let p = 5c  [c is a positive integer] [squaring on both sides ]

p² = 25c²  --------- > 2

sub p² in 1

5q²= 25c²

q² = 5c²

⇒q² is divisible by 5

=> q is divisble by 5

Thus q and p have a common factor 5

There is a contradiction  since we assumed that they are co primes

So our assumsion that √5 is rational is wrong

so √5 is an irrational