Question

Prove root 5 irrational

Answer 1

Answer:

Step-by-step explanation:

Soln- let √5 be an rational no. which can be expressed in form p/q where p,q are co-primes ( I.e their hcf is 1)

√5=p/q

Squaring on both sides

5=p^2/q ^2

P^2=5q^2…..(1)

5 divides p^2 ,therefore 5 divides p

Let p=5m..Where m is any I

p^2= 25m^2

Replacing value of p^2 from (1)

5q^2=25m^2

q^2=5m^2

5 divides q^2 .. 5 divides q

Now we get there is a common factor 5 between p and q……. This contradicts fact that p,q are co primes

That means our assumption that √5 is rational is wrong

Hence √5 is irrational

Answer 2

SOLUTION :

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.