1.

Prove root 5 irrational

Answer»

<P>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


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