Square Root of 18
2026-02-28 08:53 Diff
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Last updated on August 5, 2025

The square root of 18 is a value “y” such that when “y” is multiplied by itself → y ⤫ y, the result is 18. The number 18 has a unique non-negative square root, called the principal square root.

What Is the Square Root of 18?

The square root of 18 is ±4.24264068712, where is 4.24264068712 the positive solution of the equation x2 = 18.

Finding the square root is just the inverse of squaring a number and hence, squaring 4.24264068712 will result in 18.

The square root of 18 is written as √18 in radical form, where the ‘√’  sign is called the “radical”  sign. In exponential form, it is written as (18)1/2 
 

Finding the Square Root of 18

We can find the square root of 18 through various methods. They are:

  • Prime factorization method
  •  Approximation/Estimation method
     

Square Root of 18 By Prime Factorization Method

The prime factorization of 18 is done by dividing 18 by prime numbers and continuing to divide the quotients until they can’t be separated anymore.

After factorizing 18, make pairs out of the factors to get the square root. If there exist numbers that cannot be made pairs further, we place those numbers with a “radical” sign along with the obtained pairs

So, Prime factorization of 18 = 3 × 3 × 2   


But here in the case of 18, a pair of factor 3 can be obtained but a single 2 is remaining


So, it can be expressed as  √18 =   √(3 × 3 × 2) = 3√2


 3√2 is the simplest radical form of √18

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Square Root of 18 By Long Division Method

This method is used for obtaining the square root for non-perfect squares, mainly. It usually involves the division of the dividend by the divisor, getting a quotient and a remainder too sometimes.

Follow the steps to calculate the square root of 18:

 Step 1: Write the number 18, and draw a bar above the pair of digits from right to left.

                Step 2: Now, find the greatest number whose square is less than or equal to. Here, it is 4, Because 42=16 < 18.


Step 3 : Now divide 18 by 4 (the number we got from Step 2) such that we get 4 as quotient and we get a remainder.Double the divisor 4, we get 8, and then the largest possible number A1=2 is chosen such that when 2 is written beside the new divisor, 8, a 2-digit number is formed →82, and multiplying 2 with 82 gives 164 which is less than 200.

Repeat the process until you reach the remainder of 0.

We are left with the remainder, 34524 (refer to the picture), after some iteration  and keeping the division till here, at this point 

              Step 4 : The quotient obtained is the square root. In this case, it is 4.2426….

Square Root of 18 By Approximation


Approximation or estimation of the square root is not the exact square root, but it is an estimate. Here, through this method, an approximate value of square root is found by guessing.

Follow the steps below:


Step 1:  identify the square roots of the perfect squares above and below 18


             Below : 16→ square root of 16 = 4     ……..(i)
             Above : 25 →square root of 25 = 5     ……..(ii)


Step 2: Dividing 18 with one of 4 or 5. If we choose 4 


            We get 4.5 when 18 is divided by 4    …….(iii)

              Step 3:  find the average of 4 (from (i)) and 4.5 (from (iii))


            (4+4.5)/2 = 4.25 

            
 Hence, 4.25 is the approximate square root of 18
 

Common Mistakes and How to Avoid Them in the Square Root of 18

When we find the square root of 18, we often make some key mistakes, especially when we solve problems related to that. So, let’s see some common mistakes and their solutions

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Problem 1

if x= √18, what is x^2-8 ?

Okay, lets begin

x= √18


⇒ x2 = 18


⇒ x2-8 = 18-8

 ⇒ x2-8 = 10


Answer : 10
 

Explanation

we did the square of the given value of x and then subtracted 8 from it.
 

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Problem 2

Find the length of a side of a square whose area is 18 cm^2

Okay, lets begin

 Given, the area = 18 cm2


 We know that, (side of a square)2 = area of square


Or,  (side of a square)2 = 18


Or,  (side of a square)= √18


Or, the side of a square = ±4.226


But, length of a square is a positive quantity only, so, length of the side is 4.2426 cm.


Answer:    4.2426 cm

Explanation

We know that, (side of a square)2 = area of square. Here, we are given with the area of the square, so, we can easily find out its square root because its square root is the measure of the side of the square

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Problem 3

Simplify (√18 + √18) ⤫ √18

Okay, lets begin

(√18 + √18) ⤫ √18


= (4.2426 + 4.2426) ⤫ 4.2426


= 8.4852  ⤫ 4.2426


= 35.9993


Answer: 35.9993
 

Explanation

We first solved the part inside the brackets, i.e., √18 + √18, which resulted into 8.4852 and then multiplying it with √18 which is 4.2426 we get 35.9993
 

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Problem 4

If y=√18, find y^2

Okay, lets begin

 firstly,  y=√18= 4.2426


Now, squaring y, we get, 


y2= (4.2426)2=18


or, y2=18


Answer : 18
 

Explanation

squaring “y” which is same as squaring the value of √18 resulted to 18.

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Problem 5

Calculate (√18/4 + √18/5)

Okay, lets begin

√18/4 + √18/5

= 4.2426/ 3 +  4.2426

= 1.4142 + 0.84852

= 2.26272


Answer : 2.26272
 

Explanation

From the given expression, we first found the value of square root of 18 then  solved by simple divisions and then simple addition

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FAQs on Square Root of 18

1.How to write the square root of 18?

The square root of 18 is written as √18 
 

2.Is the square root of 18 a whole number?

 No, 4.24264068712 the square root of 18, is not a whole number.

3.Is 18 a perfect square or a non-perfect square?

18 is a non-perfect square, since 18 =(4.24264068712)2.
  

4.Is the square root of 18 a rational or irrational number?

The square root of 18 is ±4.24264068712 . So, 4.24264068712 is an irrational number, since it cannot be obtained by dividing two integers and cannot be written in the form p/q, where p and q are integers.
 

5.What is the principal square root of 18?

The principal square root of 18 is 4.24264068712, the positive value, but not -4.24264068712

6.√18 falls between which two perfect squares?

√18 = 4.24264068712 falls between two perfect squares → 4 and 9
 

Important Glossaries for Square Root of 18

  • Exponential form:  An algebraic expression that includes an exponent. It is a way of expressing the numbers raised to some power of their factors. It includes continuous multiplication involving base and exponent. Ex: 2 × 2 × 2 × 2 = 16 Or, 2 4 = 16, where 2 is the base, 4 is the exponent 
  • Prime Factorization:  Expressing the given expression as a product of its factors. Ex: 48=2 × 2 × 2 × 2 × 3
  • Prime Numbers: Numbers which are greater than 1, having only 2 factors as →1 and Itself. Ex: 1,3,5,7,....
  • Rational numbers and Irrational numbers: The Number which can be expressed as p/q, where p and q are integers and q not equal to 0 are called Rational numbers. Numbers which cannot be expressed as p/q, where p and q are integers and q not equal to 0 are called Irrational numbers. 
  • Perfect and non-perfect square numbers: Perfect square numbers are those numbers whose square roots do not include decimal places. Ex: 4,9,25 Non-perfect square numbers are those numbers whose square roots comprise decimal places. Ex :3, 8, 24

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Jaskaran Singh Saluja

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Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.

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