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Is the square root of 25 a whole number?

  • Last Updated : 05 Aug, 2021
Geek Week

The number system is a standardized system for labeling or measurements that includes different types of numbers for example prime numbers, odd numbers, even numbers, rational numbers, whole numbers, etc. These numbers can be represented in various forms and methods according to the purpose of mathematical operation. They can be written in the form of words or figures. For example, The numbers like 25 and 50 can also be written as forty and sixty-five.

A Number system or numeral system is defined as a standardized representative system to express numbers and figures. It is a unique way of representing numbers in mathematical calculations.

What are numbers?

Numbers are used in various arithmetic values applicable to carry out various arithmetic operations like addition, subtraction, multiplication, etc which are applicable in daily lives for the purpose of calculation. The value of a number is determined by the digit, its place value in the number, and the base of the number system.

Numbers generally also known as numerals are the mathematical values used for, counting, measurements, labeling and measuring fundamental quantities.

Numbers are the mathematical values or figures used for the purpose of measuring or calculating quantities. It is represented by numerals as 2,4,7, etc. Some examples of numbers are integers, whole numbers, natural numbers, rational and irrational numbers, etc.



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 are the positive counting numbers that count from 1 to infinity. The subset doesn’t include fractional or decimal values. The set of natural numbers is 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 are positive natural numbers including zero, which counts from 0 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,………………
  • 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 denoted 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 also be expressed in the fractional form in some cases. It can be expressed as 2.5,0.567, etc.
  • Real number: Real numbers are the set numbers that do not include any imaginary value. It includes all the positive integers, negative integers, fractions, and decimal values. It is generally denoted by ‘R”.
  • Complex number: Complex numbers are a set of numbers that include imaginary numbers. It can be expressed as a+bi where “a” and “b” are real numbers. It is denoted by ‘C’.
  • 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. It is denoted 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. It is denoted by ‘P’.

What is a whole number?

The subset of numbers having zero and all natural numbers are whole numbers. The whole number counts from zero to infinity. These numbers are used for counting and carrying out various arithmetic operations.

Whole numbers are the only constituents of natural numbers including zero. The subset is given by {0,1,2,3,4,5,……….}, the set does not include fractions, decimals, and negative integers.

Examples of whole Numbers

Natural numbers also known as counting numbers including zero are the part of whole numbers, such as 0,1,2,3,4,5, etc, excluding negative integers, fractions, and decimals.

0, 10, 12, 56, and 100, etc all are examples of whole numbers.

Now, let’s jump into the question

Is the square root of 25 a whole number?

Answer:



Yes, the square root of 25 is a whole number. Since, 25 is a perfect square of 5 and after square root being simplified the result would be 5, which is a whole number.

Let’s see the mathematical proof for the statement

Proof:

As we know the value 25 is a perfect square of 5

=>5×5=25

Hence, 25 is a perfect square.

Now, a square root of a perfect square can be simplified into counting number 

=>\sqrt25=\sqrt(5)^2=5

Since the subset of whole numbers include all the positive counting numbers and the value of the square root of 25 is derived to be 5.

The square root of 25 is a whole number.



Similar Questions

Question 1: Is the square root of 4 a whole number?

Answer:

Yes, the square root of 4 is a whole number. Since, 4 is a perfect square 2 and after square root being simplified the result would be 2, which is a whole number.

Question 2: Can a square root be a whole number?

Answer:

Yes, if the square root is a perfect square of any real number then, a square root can be a whole number.

Question 3: Is a square root of 25 a  rational number?

Answer:

The square root of 25 is equal to 5 as 25 is a perfect square of 5. Hence, as 5 is a integer and can be expressed in the form of p/q root 25 is rational number.

Question 4: Can root 16 be a whole number?

Answer:

Yes, the square root of 16 is a whole number. Since, 16 is a perfect square of 4 and after square root being simplified the result would be 4, which is a whole number.

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