Question

prove that√7 is a irational​

Answer 1

answer

step by step

since √7 =rational so

√7 =p/q and q not equal to 0

so√7/1 =p/q

hence proved

√7 =p/q

our contradiction is wrong so √7 =not (p/q)

please mark me as brainliest

Answer 2

let us assume that √7 is a rational

√7=a/b,where a,b are coprimes and b is not equals to 0

squaring on both side

√7²=a²/b²

7=a²/b²

b²7=a²

b²=a²/7 ----------equaltion 1

(if p divides a² then p divides a) similarly here from equation 1,if 7 divides a² then 7 divides a

let a/7=k

a=7k in equation 1

b²= (7k)²/7

b²=49k²/7

b²=7k²

k²=b²/7----------equation 2

here from equation 2,if 7 divides b² then 7 divides b

from equation 1 and 2,7 divides both a² and b²,but here a,b are so primes

so our assumption is wrong

therefore √7 is an irrational number

this is the exact answer,hope this is helpful