If x = √p + √q, where p and q are distinct primes then which of the following is a rational number?

A. (√p + √q)²

B. (√p - √q)²

C. (√p + √q)(√p - √q)

D. None of these

OR

Write three irrational numbers between √2 and √3

We have

(√p + √q)² = p + q + 2√p√q

= p + q + 2√pq

Now ‘p’ and ‘q’ are distinct primes therefore √pq can’t be a perfect square and it’s an irrational number.

Similarly, (√p - √q)² is an irrational number.

But, (√p + √q) (√p - √q) = p – q is a rational number

OR

There are countless irrational numbers between any two real numbers.

Now, we have

√2 = 1.41….

√3 = 1.73…

So, we can write any three rational numbers for example

1.42420420042000…

1.50500500050000…

1.71711711171111…