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Are square roots whole numbers?

  • Last Updated : 03 Sep, 2021

Numerals are the mathematical figures used in financial, professional as well as a social field in the social world. The digits and place value in the number and the base of the number system determine the value of a number. Numbers are used in various mathematical operations as summation, subtraction, multiplication, division, percentage, etc which are used in our daily businesses and trading activities.

Numbers are the mathematical figures or values applicable for counting, measuring, and other arithmetic calculations. Some examples of numbers are integers, whole numbers, natural numbers, rational and irrational numbers, etc.

The number system is a standardized method of expressing numbers into different forms being figures as well as words. It includes different types of numbers for example prime numbers, odd numbers, even numbers, rational numbers, whole numbers, etc. These numbers can be expressed in the form on the basis of the number system used.

The elementary system to express numbers is called a number system. It is the standardized method for the representation of numerals in which numbers are represented in arithmetic and algebraic structure.

Types Of Numbers

There are different types of numbers categorized into sets by the number system. The types are described below:

  • Natural numbers: Natural numbers counts from 1 to infinity. They are the positive counting numbers that are represented by ‘N‘. It is the numbers we generally use for counting. The set of natural numbers can be represented as N={1,2,3,4,5,6,7,……………}
  • Whole numbers: Whole numbers count from zero to infinity. Whole numbers do not include fractions or decimals. The set of whole numbers is represented by ‘W‘. The set can be represented as W={0,1,2,3,4,5,………………}
  • Rational numbers: Rational numbers are the numbers that can be expressed as the ratio of two integers. It includes all the integers and can be expressed in terms of fractions or decimals and is represented by ‘Q‘.
  • Irrational numbers: Irrational numbers are numbers that cannot be expressed in fractions or ratios of integers. It can be written in decimals and have endless non-repeating digits after the decimal point. They are represented by ‘P‘.
  • Integers: Integers are the set of numbers including all the positive counting numbers, zero as well as all negative counting numbers which count from negative infinity to positive infinity. The set doesn’t include fractions and decimals. The set of integers is represented by ‘Z‘. The set of integers can be represented as Z={………..,-5.-4,-3,-2,-1,0,1,2,3,4,5,………….}
  • Decimal numbers: Any numeral value that consists of a decimal point is a decimal number. It can be expressed as 2.5,0.567, etc.
  • Real number: The set of numbers that do not include any imaginary value and are constituent of all the positive integers, negative integers, fractions, and decimal values are real numbers. It is generally denoted by ‘R‘.
  • Complex numbers: They are a set of numbers that include imaginary numbers are complex numbers. It can be expressed as a+bi where “a” and “b” are real numbers. It is denoted by ‘C‘.

What are Squares?

Squares are the mathematical values that are computed by multiplying a number by itself. So, if there’s a number x then its square will be calculated by multiplying x by itself i.e. x × x = x2. Similarly, the square root of x2 will be the number x.

What is a Perfect Square?

A perfect square is a number that can be represented as the product of two equal integers.

For example, 36 is a perfect square as it has two equal integers i.e. (6 × 6 = 36), whereas 21 is not a perfect square because it does not have two equal integers i.e. (7 × 3 = 21).

Are square roots whole numbers?


Squares are numbers that are computed by multiplying a number by itself. When a whole number is multiplied by itself, the result is always a whole number, which is termed as a perfect square. 

Hence, square roots of perfect squares are always whole numbers. 

For example, square root of 36 will be 6 which is a whole number. Since, 36 = 6 × 6, it is a perfect square. 

Similar Questions

Question 1: Is 441 a perfect square?


In the above-given question first, we have to find the factors of 441.

So, the factors of 441 are 3 × 7 × 3 × 7.

In the factors of 441, we have the pairs (3×3) and (7×7) and there is no single digit left alone. Therefore, 441 is a perfect square.

Question 2: Is 500 a perfect square?


In the above-given question first, we have to find the factors of 500.

So, the factors of 500 are  2 × 2 × 5 × 5 × 5.

In the factors of 500, we have the pairs (2×2) and (5×5) but one 5 is left alone. Therefore, 500 is not a perfect square.

Question 3: Is 324 a perfect square?


In the above-given question first, we have to find the factors of 324.

So, the factors of 324 are 2 × 2 × 3 × 3 × 3 × 3.

In the factors of 324, we have pairs (2×2), (3×3), and (3×3) and there is no single digit left alone. Therefore, 324 is a perfect square.

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