Question

Prove that √5 is irrational...........​

Answer 1

we can prove this by indirect proof

let's assume that the number√5 is rational..... (1)

that is,

it can be denoted in fractional or p/q form

therefore,

√5=p/q

therefore

√5q=p

but on LHS,

number is irrational and on RHS number is rational....(2)

statement(2) is contradictory to (1)

therefore our assumption is wrong.

hence proved that,

√5 is irrational

Answer 2

to prove root 5 is irrational ...

lets assume root 5 as rational

so.. root 5 = p/q

where p and q are co-prime number

root 5 = p/q

by squaring both the sides

5 = (p/q)^2

5= p^2 /q^2

q^2 = p ^2 / 5 ........(1)

by eqn (1) we get to know that ..

p^2 is divisible by 5

so p is also divisible by 5

now consider p = 5m

so .. by putting value in (1)

q^2 = (5m)^2 / 5

q ^2 = 25 m ^2 / 5

q ^2 = 5 m^2

q ^2 /5 = m ^2 ......(2)

by eqn (2) we get to know that

q^2 is divisible by 5

so q is also divisible by 5

therefore by eqn (1) and (2) we can say that p and q have factor more than two numbers . and hence they are not co-prime number

since our assumption was wrong and it contradict the fact thatt root 5 is irrational

hope its helpful plssss mark as brainliest

Answer 3

hope it will help you