Question

prove that the following numbers are irrational a 4+2under root​

Answer 1

Let us assume, to the contrary, that 4 + √2 is a rational number.

Now,

4 + √2 = p/q [ Where p and q are co - primes and q is not equal to zero ]

So,

⇒ 4 - p/q = √2

⇒ √2 = 4 - p/q

Since, p and q are integers, we get 4 - p/q is rational number and so, √2 is rational number.

But this contradicts the fact that √2 is irrational number.

This shows that our assumption is incorrect.

So, we concluded that 4 + √2 is an irrational number.

Answer 2

$\huge\mathfrak{Answer:}$

Given:

• We have been given a number 4 + √2.

To Find:

• We need to prove that it is irrational.

Solution:

Let us assume that 4 + √2 is a rational number.

Therefore, it can be written in the form of p/q where p and q are coprime.

4 + √2 = p/q

=> √2 = p/q - 4

=> √2 = (p - 4q)/4 [√2 is a rational number as it is written in the form of p/q]

But, this contradicts the fact that √2 is irrational.

Hence, our assumption that 4 + √2 is rational was wrong.

Hence, 4 + √2 is irrational.