Square root of 144
2026-02-28 21:44 Diff
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Last updated on August 5, 2025

The square root of 144 is the inverse operation of squaring a value “y” such that when “y” is multiplied by itself → y ⤫ y, the result is 144. It contains both positive and a negative root, where the positive root is called the principal square root.

What Is the Square Root of 144?

The square root of 144 is ±12.The positive value, 12 is the solution of the equation x2 = 144. As defined, the square root is just the inverse of squaring a number, so, squaring 12 will result in 144.  The square root of 144 is expressed as √144 in radical form, where the ‘√’  sign is called “radical”  sign. In exponential form, it is written as (144)1/2  
 

Finding the Square Root of 144

We can find the square root of 144 through various methods. They are:

  • Prime factorization method
  • Approximation/Estimation method
     

Square Root of 144 By Prime Factorization Method

The prime factorization of 144 involves breaking down a number into its factors. Divide 144 by prime numbers, and continue to divide the quotients until they can’t be separated anymore. After factorizing 144, make pairs out of the factors to get the square root. If there exists numbers which cannot be made pairs further, we place those numbers with a “radical” sign along with the obtained pairs

So, Prime factorization of 144 = 2 × 2  × 2 × 2 × 3 × 3   


for 144, two pairs of factor 2 and one pair of factors 3 can be obtained.


So, it can be expressed as  √144 = √(2 × 2  × 2 × 2 × 3 × 3) = 2 × 2 × 3 = 12


12 is the simplest radical form of √144

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Square Root of 144 By Long Division Method

This is a method 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 144:


Step 1: Write the number 144 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 1. Here, it is1 because 12=1


Step 3: now divide 1 by 1 (the number we got from Step 2) such that we get 1 as a quotient, and we get a remainder.  Double the divisor 1, we get 2, and then the largest possible number A1=2 is chosen such that when 2 is written beside the new divisor 2, a 2-digit number is formed →22, and multiplying 2 with 22 gives 44, which is equal to 0 on subtracting from 44.


Repeat this process until you reach the remainder of 0. 

Step 4: The quotient obtained is the square root of 144. In this case, it is 12.

Square Root of 144 By Subtraction Method

roots through the repeated subtraction method. Furthermore, we just have to subtract consecutive odd numbers from the given number, starting from 1. The square root of the given number will be the count of the number of steps required to obtain 0. Here are the steps:

Step 1: take the number 144 and then subtract the first odd number from it. Here, in this case, it is 144-1=143


Step 2: we have to subtract the next odd number from the obtained number until it comes zero as a result. Now take the obtained number (from Step 1), i.e., 143, and again subtract the next odd number after 1, which is 3, → 143-3=140. Like this, we have to proceed further.


Step 3: now we have to count the number of subtraction steps it takes to yield 0 finally. 


Here, in this case, it takes 12 steps 


So, the square root is equal to the count, i.e., the square root of 144 is ±12.

Common Mistakes and How to Avoid Them in the Square Root of 144

When we find the square root of 144, 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

Find √(144⤬4) ?

Okay, lets begin

√(144⤬4)

= 12 ⤬2

= 24


Answer : 24
 

Explanation

 firstly, we found the values of the square roots of 144 and 4, then multiplied the values.

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Problem 2

What is √144 multiplied by 14 ?

Okay, lets begin

 √144 ⤬ 14

= 12⤬ 14

= 168


Answer:168 
 

Explanation

 finding the value of √144 and multiplying by 14.
 

Well explained 👍

Problem 3

Find the radius of a circle whose area is 144π cm².

Okay, lets begin

 Given, the area of the circle = 144π cm2


Now, area = πr2 (r is the radius of the circle)


So, πr2 = 144π cm2


We get, r2 = 144 cm2


r = √144 cm


Putting the value of √144 in the above equation, 


We get, r = ±12 cm


Here we will consider the positive value of 12.


Therefore, the radius of the circle is 12 cm.


Answer: 12 cm.
 

Explanation

 We know that, area of a circle = πr2 (r is the radius of the circle) According to this equation, we are getting the value of “r” as 12 cm by finding the value of the square root of 144
 

Well explained 👍

Problem 4

Find the length of a side of a square whose area is 144 cm²

Okay, lets begin

Given, the area = 144 cm2


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


Or,  (side of a square)2 = 144


Or,  (side of a square)= √144


Or, the side of a square = ± 12.


But, the length of a square is a positive quantity only, so, the length of the side is 12 cm.


Answer: 12 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
 

Well explained 👍

Problem 5

Find √144 / √36

Okay, lets begin

 √144/√36

= √(144)/√(36)

=12/6  

= 2


Answer : 2 
 

Explanation

 we firstly found out the values of √144 and √36, then divided  .
 

Well explained 👍

FAQs on 144 Square Root

1.How many times does 9 go into 144?

9 goes into 144 by 16 times 
 

2.Can 144 be divided by 9?

Yes, 144 is divisible by 9
 

3.Is 144 a perfect square or non-perfect square?

 144 is a perfect square, since 144 =(12)2.
 

4.Is the square root of 144 a rational or irrational number?

The square root of 144 is ±12. So, 12 is a rational number, since it can be obtained by dividing two integers and can be written in the form p/q, where p and q are integers.
 

5.What are the factors of 144 ?

Factors of 144 are 1,2,3,4,6,8,9,12,16,18,24,36,48,72 and 144
 

Important Glossaries for Square Root of 144

  • 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, 24 = 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

About the Author

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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