Choose which set or sets the following number belongs to. Be sure to account for ALL sets.
√20
rational numbers
irrational numbers
real numbers
rational numbers, real numbers
irrational numbers, real numbers
√20 is a rational number and a real number.
To determine which set or sets the number √20 belongs to, we need to understand the properties of each set.
1. Rational numbers: Rational numbers are numbers that can be expressed as a fraction of two integers. They include integers, fractions, terminating decimals, and repeating decimals.
2. Irrational numbers: Irrational numbers cannot be expressed as a fraction of two integers. They include numbers with non-repeating, non-terminating decimals, such as √2 and π.
3. Real numbers: Real numbers include both rational and irrational numbers. They represent all possible values on the number line.
Now, let's analyze √20:
√20 is approximately 4.472 when rounded to three decimal places. Since it is a non-repeating, non-terminating decimal, we can conclude that it is an irrational number.
Therefore, the number √20 belongs to the sets: irrational numbers, real numbers.
To determine which set or sets the number √20 belongs to, we need to analyze its properties.
1. Rational numbers:
A rational number is any number that can be expressed as a fraction of two integers. The square root of 20 (√20) is NOT a rational number because it cannot be expressed as a fraction.
2. Irrational numbers:
An irrational number is any number that cannot be expressed as a fraction. The square root of 20 (√20) is an irrational number because it cannot be expressed as a fraction.
3. Real numbers:
Real numbers include both rational and irrational numbers. Since √20 is an irrational number, it is also a real number.
Based on the above analysis, the number √20 belongs to the following set or sets:
- Irrational numbers, Real numbers.