Question

3. Prove that the following are irrationals:
(I) 1/√2
(ii) 7√5
(iii) 6+√2​

Answer 1

Step-by-step explanation:

(i) we can assume that let, 1/root 2 is a rational number.

1/root 2 =p/q

by squaring both sides

1/2=p2/q2

1/2q2=p2

2 is a factor of p2 and 2 will be factor of p also.

q= 1/root 2

by squaring both sides

q2= 1/2

2 is a factor of q2 and 2 will be factor of q

= 2 is a factor of q and p both so our assumption is wrong that 1/root 2 is a rational number.

hence proved

(ii) and (iii) part will same as (i).

thank u

Answer 2

See the photo attached