Question

Prove that under root 5 and 3 under root5 are irrational
numbers.​

Answer 1

let root 3 is a rational number.

root 3=a/b where a and b are co- prime and b is not eqal to 0

root 3 b= a

sqaring both side

3b sqare=a sqare

since a sqare is divisible by 3

a is also divisible by 3

let a=3c

putting, we get

3b sqare= 3c whole sqare

3b sqare= 9c sqare

bsqare=3c sqare

b sqare is divisible by 3

b is also divisible by 3

hence our assumption is wrong

root 3 is an irrationl number

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