Question

prove that√2,√3,√5,√p,√q are irrational number.​

Answer 1

Answer:

We are going to prove it by contradiction.

First, let's assume 2√2 to be rational.

then,

2√2 = p/q, where q≠0 and p, q be co primes

then,

p = 2q√2. ( squaring on both sides)

p²=8q²

let's take 4q² as y² (because 4q²=(2q)²). *****(1)

then we get

p² = 2y²

here we see that p² is divisible by 2, so p is also

divisible by 2. .*****(2)

from (1) and (2), we see that both q and p are divisible

by 2. but this is contradicting that p, q are co primes

So, the assumption that 2√2 is rational is false.

hope it helps. if there are any corrections please inform me. (◠‿◕)

SIMILARLY WE CAN SOLVE ROOT  3, ROOT 5, ROOT P, ROOT Q IS IRRATIONAL BY PUTTING THESE AT PLACE OF 2.......

PLZ MARK ME AS A BRAINLIEST AND ALSO FOLLOW BHI KRO YRRRRRRR

Step-by-step explanation:

Answer 2

Answer:

root 5 can be written as a/b

root 5 = a/b

root 5b=a

(root 5b²)=a²

5b²= a²