Question

step by step solution plzz​

Answer 1

Step-by-step explanation:

Let us assume that 3√2/4 is rational. Hence it can be written in the form of p/q (q is not equal to zero) where p and q are co-primes.

3√2/4=p/q

Squaring both sides

9×2/16=p²/q²

9/8=p²/q²

9q²=8p²

Now, p² is divisible by q², this means p² is also divisible by q.

Let p=3x

=> 9q²=8(3x)²

9q²=8(9x²)

q²=8x²

Since, q² is divisible by x², this means q² is also divisible by x.

Let q=4y

=> (4y)²=8x²

16y²=8x²

2y²=x²

This means that p and q have some common factor.

This contradicts the fact that a and b are co-primes.

This contradiction has arisen due to our incorrect assumption of 3√2/4 as rational.

Hence, 3√2/4 is irrational.