Answer:
The product of the square root of a prime number and a nonzero rational number is a irrational number.
Step-by-step explanation:
Given that,
When is the product of the square root of a prime number and a nonzero rational number a irrational number.
We know that,
Prime number :
Prime number is that number whose has a two factor. first factor is one and second is themselves.
The square root of a prime number is irrational number.
Rational number :
Rational number is that number which is in fraction form.
For example :
Here, p and q are integers
We need to proof the product of the square root of a prime number and a nonzero rational number is a rational number
Using given data
Suppose, the square root = √5
Rational number =
We need to calculate the product of the square root of a prime number and a rational number
Using formula of product
Where, P = square root of a prime number
Q= rational number
Put the value into the formula
Hence, The product of the square root of a prime number and a nonzero rational number is a irrational number.