What sets of numbers does the square root of 36 belong to? 1. Real 2. Rational 3. Irrational 4. Natural 5. Whole 6. Interger
The correct answer and explanation is:
Correct Answer:
The square root of 36 belongs to the following sets of numbers:
1. Real, 2. Rational, 4. Natural, 5. Whole, 6. Integer
Explanation:
The square root of 36 is √36. When this is simplified, it equals 6 because 6 multiplied by itself (6 × 6) equals 36. The result is a whole number, which makes it part of several number sets.
First, it is a real number because all rational and irrational numbers fall under the category of real numbers. Since √36 is a known value and not imaginary, it is real.
Second, it is a rational number. A rational number is any number that can be written as a fraction or ratio of two integers. In this case, 6 can be written as 6/1, which makes it rational.
Third, it is not an irrational number. Irrational numbers cannot be written as a fraction of two integers, and they have non-repeating, non-terminating decimal parts. The number 6 is exact and whole, so it is not irrational.
Fourth, it is a natural number. Natural numbers are the set of positive counting numbers such as 1, 2, 3, and so on. Since 6 is a positive number used for counting, it qualifies as natural.
Fifth, it is a whole number. Whole numbers include all natural numbers and zero. Since 6 is a positive whole number, it is included in this set.
Lastly, 6 is an integer. Integers include all whole numbers and their negative counterparts, such as -3, 0, and 7. Since 6 is a whole number without a fractional or decimal part, it is an integer.
Therefore, √36 belongs to the real, rational, natural, whole, and integer sets. It does not belong to the irrational set.