Question

Prove that 2√3÷5 is irrational number

Answer 1

let us assume that 2√3/5 is a rational number. then we can write it as p/q where p and q are co-primes and q is not equal to zero.

=> 2√3/5 = p/q

=>2√3 = 5p/q

=>√3 = 5p/2q

now, as p, q, 2, 5 are all rationaal no. RHS is rational, so LHS is also rational.

but this contradicts the fact that √3 is irrational. this contradiction has arose due to our wrong assumption that 2√3/5 is rational.

Hence, our assumption is wrong and 2√3/5 is irrational.

Answer 2

let 2√3\5is a rational number

so we can write in form of p/q

where p & q are co prime number

p/q=2√3\5

5p/q=2√3

5p/2q=√3

5p/2q is rational number

bcoz p & q are co prime number

but √3 is irrational number

so our assume is not correct

then 2√3/5 is irrational number

✔️✔️

☺️ThAnKs✳️✳️

@ArJuN$❇️❇️❤️❤️