Question

prove that √5 is an irrational number​

Answer 1

Answer:

let √5 is rational number

Now, √5= a/b ( b is not equal to 0 and a or b are coprime numbers)

√5=a/b

b√5=a

squaring both sides

(b√5)square = (a) square

b2 ×5 = a2

b2= a2/5.....(1)

Here 5 divides a2 so it also divide a

Now let, a=5c

put value of a in equation (1)

b2 =(5c)2 /5

b2= 25c square /5

b2= 5csquare

b2/5 = c2

here 5 divides b2 so it also divides b

from above , our supposition is wrong. This contradicts the fact that √5 is an irrational number.

hence proved..

hope it help u..

Answer 2

Answer:

Step-by-step explanation: