Answer and Step-by-step explanation:
The number π√4 is irrational.
A rational number is a number that can be expressed as a fraction of two integers, where the denominator is not zero. An irrational number is a number that cannot be expressed as a fraction of two integers.
In the case of π√4, the square root of 4 is 2, which is an integer. However, π is an irrational number, so π√4 is also an irrational number.
Here is a proof that π√4 is irrational:
Assume that π√4 is rational. Then, it can be expressed as a fraction of two integers, a/b, where a and b are integers and b is not equal to zero.
Squaring both sides of the equation, we get:
π^2 * 4 = a^2 / b^2
This equation implies that π^2 is an integer. However, π^2 is not an integer, because π is an irrational number.
Therefore, our assumption must be false, and π√4 cannot be rational.
Therefore, the number π√4 is irrational.