Question

9 th question it is needed

Answer 1

Answer: Its a Proof

Step-by-step explanation:

Given, √(ab) is an irrational number.

Let √a + √b is rational.

So, √a + √b can be written as p/q form where q ≠ 0

=> √a + √b = p/q

Squaring on both side, we get

=> (√a + √b)2 = (p/q)2

=> a + b + 2√a * √b = p2 /q2

=> a + b + 2√(ab) = p2 /q2

=> 2√(ab) = p2 /q2 - (a + b)

=> √(ab) = {p2 /q2 - (a + b)}/2   ...........1

Since √a + √b is rational, So √a , √b is also rational.

But LHS of equation 1 is irrational.

which contradict our assumption.

Hence, √a + √b is an irrational number.

This is your required Proof of the Question , Hope you understood it!!

Answer 2

ANSWER

Plz, refer to the attachment for the proof with a full explanation.

Remember

1)Any rational number can be expressed in the form $\dfrac{p}{q}$ where q not equal to zero.

2)We use the assumption method to prove that a number is irrational.

3)Co primes are the pair of numbers which has a common factor of 1 only.