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Is √16 an irrational number?

  • Last Updated : 05 Aug, 2021

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. Let’s look at the different types of numbers found in the number system.

The Real Numbers are the Numbers that consist of ALL THE NUMBERS ie., all of the Rational Numbers and Irrational 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 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 are the Natural Numbers with Including an extra number zero. Integers set are the Number set that consist of negative and positive numbers including zero.

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Rational and Irrational Numbers

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 also rational it can be expressed in p/q form ie. 2/1 

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 never terminates (we generally round off the value to 3.14), it is an Irrational Number.
  • Square Roots of the Numbers which are not Perfect Squares are always Irrational Numbers like √2 is 1.41421356237309…
  • Square Roots of Perfect Squares are always Rational

Is √16 an Irrational Number?

As mentioned above, the square roots of the perfect square are always Rational. Suppose √x is given and y2= x, where y is a rational number, √x is also a Rational number. 

√16 is Rational because, its value is 4, which can be expressed as a Ratio of Two Numbers like 4/1 or 8/2.

Therefore √16 is NOT AN  IRRATIONAL NUMBER

Similar Examples

Question 1: Is √8 an Irrational number?

Solution: 

√8 = 2√2  = 2× (1.14142135….) is an Irrational Number because when a number is multiplied with an Irrational Number results in an Irrational Number.

Question 2: Is √4 an Irrational number?

Solution:

√4  = 2 = 2/1 is rational it can be expressed in p/q form ie. 2/1

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