What is 81 square root classified as? (List all that apply)
a) Natural
b) Whole
c) Integer
d) Rational
e) Irrational
f) Real
The Correct Answer and Explanation is :
The square root of 81 is classified as:
a) Natural
b) Whole
c) Integer
d) Rational
f) Real
Explanation:
The square root of 81 is 9, which can be broken down as follows:
- Natural Numbers: Natural numbers are positive integers used for counting (1, 2, 3, …). Since 9 is positive, it is classified as a natural number.
- Whole Numbers: Whole numbers include all natural numbers plus zero (0, 1, 2, …). Since 9 is a natural number, it is also a whole number.
- Integers: Integers include all whole numbers, both positive and negative, as well as zero. Since 9 is a positive number and whole, it is classified as an integer.
- Rational Numbers: Rational numbers are numbers that can be expressed as the quotient of two integers, where the denominator is not zero. The number 9 can be expressed as ( \frac{9}{1} ), making it a rational number.
- Irrational Numbers: Irrational numbers cannot be expressed as a fraction of two integers and have non-repeating, non-terminating decimal expansions. Since 9 is not irrational, it does not fall into this category.
- Real Numbers: Real numbers encompass all rational and irrational numbers. Since 9 is a rational number, it is also classified as a real number.
In summary, the square root of 81, which is 9, qualifies as a natural number, whole number, integer, rational number, and real number. Each classification reflects different aspects of the number’s properties in mathematics, showing its versatility and fundamental nature in the number system.