Is this product rational or irrational
5.5√5
This product is irrational because the square root of 5 is an irrational number and multiplying an irrational number (5.5) with an irrational number results in an irrational number.
To determine whether the product 5.5√5 is rational or irrational, we need to know if the square root of 5 is rational or irrational.
The square root of 5 is an irrational number because it cannot be expressed as a fraction and its decimal representation does not terminate or repeat.
Since 5.5 is a rational number (because it can be expressed as a fraction: 11/2), and the product of a rational number and an irrational number is always irrational, 5.5√5 is an irrational number.
To determine if the product 5.5√5 is rational or irrational, we need to understand the characteristics of rational and irrational numbers.
- Rational numbers can be expressed as a fraction p/q, where p and q are integers and q is not equal to zero. Rational numbers can be either terminating (finite decimal) or repeating (infinite decimal) when expressed as decimals.
- Irrational numbers cannot be expressed as a fraction. They are non-repeating and non-terminating when expressed as decimals.
Now, let's determine if 5.5√5 is rational or irrational.
First, we simplify the expression by multiplying the rational number 5.5 with the irrational number √5:
5.5 * √5 = √5 * 5.5
Next, we are left with the product of an irrational number (√5) and a rational number (5.5). It is important to note that the product of a rational and an irrational number is always irrational.
Therefore, the product 5.5√5 is an irrational number.