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Is the square root of 16 a whole number?

  • Last Updated : 17 Aug, 2021
Geek Week

A Number system is a way of representing numbers. Representation of numbers is done by using digits or symbols. The Numbers that are represented by digits or symbols have the value and the value depends on the place, base, and value of the digits used. There are different types of numbers in the decimal number system based on their characteristics, some of them are explained here,

Types of Numbers

In the decimal number system, that is, the number system with base 10, there are different characteristics of numbers, for instance, real numbers, complex numbers, whole numbers, natural numbers, prime numbers, and so on. Let’s take a look at some of the important definitions,

The Real Numbers

The Real numbers are the numbers that consist of all the numbers ie., all of the Rational Numbers and Irrational Numbers. For example, 3, 7.888888, 3.14, etc.

The Complex Numbers

The Complex numbers are the numbers that are represented in (a+ib) form where b≠0, where a and b are Real Numbers and i is an imaginary unit with the value √-1. When the value is b. It is a Real number since in (a+ib) b=0 then a+i*0 = a which is a real Number.

The Integers

Integers set are the Number sets that consist of negative and positive numbers including zero. All the basic operations of the number system ie., Addition, Multiplication, Subtraction except Division will result in an Integer. The division may or may not result in an Integer because when a smaller numerator and bigger denominator are used in division. It results in a fraction, that may be Rational Or Irrational

Irrational Number

A Number is called irrational if it cannot be expressed in the form of p/q, where p and q are Integers. In other words, if it cannot be expressed as a ratio of two numbers. When a number is expressed in Decimal form, if it never terminates it is an Irrational number. For example,

  • the Value π(PI) is 3.1415926…. the value is non-terminating and non-repeating.
  • √2 is 1.41421356237309…, basically, the square root of a number that is not a perfect square is irrational.
  • Square Roots of Perfect Squares are always Rational, for example, √9, √16, etc.

Rational Number

A Number is called Rational if it can be expressed in the form of p/q, where p and q are Integers. In other words, if it can be expressed as a ratio of two Numbers. When a number is expressed in decimal form, if it terminates it is a Rational number. Some numbers that are Never Terminating But are Recurring are Rational Numbers. For example, 0.0833333… it is the decimal representation of 1/12 is a Rational Number. √4 is rational it can be expressed in p/q form ie. 2/1

The Natural Numbers

The Natural Numbers are the Numbers that start from 1 and counts to Infinity. 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11…..up to Infinity are Natural Numbers. It is a Subset of Whole Numbers.

The Whole Numbers

The Whole numbers are the Natural numbers with including an extra number zero ie., the numbers that start from 0 and counts to infinity are called Whole numbers. It is a Superset of Natural numbers. Whole numbers are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11….up to Infinity.

Square of a number 

The Square of a number is defined as a number multiplied by itself. It is also known as a number raised to the power of 2. When whole numbers are squared it results in Perfect Squares. For example,

  • Square of Number 10: As per definition, the number multiplied by itself, 10 multiplied by itself  = 10*10 = 100. Therefore, the square of 10 is 100.
  • Square of Number 8 is 8×8 = 64
  • Square of Number -4 is (-4) × (-4)  = 16
  • Square of fraction (3/4) is (3 × 3)/(4 × 4) = 9/16.

Note Square of a Number is always positive.

Square Root 

The Square Root of a number is the value that is squared or multiplied by itself to get the original number. Square Root of a number is also defined as a number raised to the power of 1/2. Square Root of perfect Square is always the whole number. The Square root of a nonperfect square always leads to decimal value. The symbol of the square root is √ . The  Square root of a negative number is imaginary. Square Root of number -x i.e, √-x = √(i2)×x = i√x (i2 = -1 ) i is imaginary number .

Note Square Root of a Negative Number Results in Complex Numbers or Imaginary Numbers

Is the square root of 16 a whole number?

Square Root of 400 : √400 = √(20)2 = 20.

or when 400 is raised to the power of 1/2 i.e, (400)(1/2) = 20.

Square Root of 8 is : √8 = √2×(22) = 2√2.

Square Roots of Numbers may be or may not be Whole Numbers. Square Root of 36 is 6 which is a Whole Number whereas, Square Root of 27 is 3√3 which is not a whole Number because the value of √3 is 1.732… which multiplies 3 gives a Decimal Number. Since the Square root of Perfect Squares is always the whole number.

  • Square Root of 4 i.e, √4 = 2. hence,√4 is a whole number

Square Root of 16 i.e, √16 is 4 is a WHOLE NUMBER. Therefore Square Root of 16 is a whole number

Similar Problems

Question 1: What is the square root of 81/25?


\sqrt\frac{81}{25}= \frac{9}{5}

Hence, the square root of 81/25 is 9/5.

Question 2: What is the square root of 36/49? Is it a whole number?


√(36/49) = \sqrt\frac{6^2}{7^2}= √(6/7)2 = 6/7. Square Root of 36/49 value is 6/7 which leads to a Decimal value Therefore \sqrt\frac{36}{49} is not a whole number.

Question 3: What is the square root of 18?


3√2 is not a whole number, because √2 = 1.414.. when multiplied by 3 leads to a decimal value.

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