Question

(5+√5) (5-√5)
prove step by step whether it is a rational number or not

Answer 1

This can be written as a^2-b^2, therefore it can be written as 25-5 which is equal to 20.
Hence, this is a rational number as it can be written as 20/1.

Answer 2

Answer:

Rational number

Step-by-step explanation:

Given: (5 + √5)(5 - √5)

∴ (a + b)(a - b) = a² - b²

= (5)² - (√5)²

= 25 - 5

= 20

= 20/1.

∴Any number that can be expressed in the form of p/q are rational numbers.

Here, 20 is a rational number because it can be expressed in the form of p/q{where p,q are integers and q is not equal to zero}.

Therefore, (5 + √5)(5 - √5) generates a rational number.

Hope it helps!