Question

prove that
that following are irrational numbers..
√7​

Answer 1

Step-by-step explanation:

ie, √7=p/q. we divide by the common factor to get √7 = a/b were a and b are co-prime number. that is a and b have no common factor. that is a and b have atleast one common factor 7.

Hope this helps you

Answer 2

Answer:

Let √7 be rational. Then we can write it as p/q where p and q are coprimes and q is not equal to 0. Then ✓7=p/q => √7q=p => squaring both sides we get: 7q^2=p^2 => 7 divides p square => 7 divides p as well. Since 7 dives p that means it is prime factor of p. So we can write p as 7n where n is any whole number. putting it in previous equation we get:

7q^2=(7n)^2 => q^2 = 7n^2 => 7 divides q^2=> 7divides q.

So we can clearly see 7 divides q and p both. So our assumption that p and q are coprimes was wrong. Therefore √7 is irrational.

Hope it helps you.