Question

What is √n , if n is not a perfect square number

Answer 1

Answer:

Route n is not a rational number, if n is not a perfect square number.

Step-by-step explanation:

If n is not a perfect square route n is irrational.

Let on the contrary say it is rational.

Then,

Route n = p/q [where p and q are co-prime]

n = p^2/q^2

p^2 = nq^2

This show p divides q which is contradiction.

Hence, route n is irrational if n is not a perfect square.

hope it helps you✌

Answer 2

If n is a natural number, then$\sqrt{n}$   is also always a rational number and natural number.

Step-by-step explanation:

• A number is advantageous if it can be written as a fraction where the denominator and numerator are integers and the denominator is a non zero number.

$\sqrt{4}$ =2 where 2 is a rational number.Here n is perfect square the   $\sqrt{n}$  is rational number  

$\sqrt{5}$ =2.236.. is not rational  number But it is irrational number . here n is not a perfect square the $\sqrt{n}$ is  irrational  number

So $\sqrt{n}$  is not irrational number if n is perfect square.  

• $\sqrt{n}$ is an integer and n is a square number, that is, we can conclude about some integer. So if n is a square number, then $\sqrt{n}$ is favorable. Now suppose that n is not a square number and I want to show that the square root of a non-squared number is irrational.