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Square Root of 144
Kyrie plans on making a squareshaped half basketball court in his backyard. He kept the area of the court as 144 square feet. Now he is trying to figure out the sides of the court. For determining the side of a squareshaped object, one should find the square root of the given area. The square root of 144 is the number (Integer) which when multiplied by itself results in 144. In this minilesson, we will calculate the square root of 144 by prime factorization and long division method along with a few interesting problems.
 Square root of 144: 12
 Square of 144: 20736
What Is the Square Root of 144?
 The square root of a number is the number (integer) which when multiplied by itself results in the original number.
 144 = a × a = 12^{2}
 Then a = √144 = √(12 × 12)
 12 × 12 = 144 or 12 × 12 = 144
 The square root of 144 is +12 or 12
 This shows that 144 is a perfect square.
Is Square Root of 144 Rational or Irrational?
 A rational number is defined as a number that can be represented in the ratio of two integers, that is, p/q where q ≠ 0.
 12 and 12 can be written as 12/1 and 12/1
 Both numbers can be expressed in the form of rational numbers.
 So, the square root of 144 is a rational number.
How to Find the Square Root of 144?
The square of 144 can be calculated using the prime factorization method, long division method, or repeated subtraction method.
Square Root of 144 by Prime Factorization Method
The following steps can be followed to find the square root of 144 using prime factorization:
Step 1. Determine the prime factors of 144.
144 = 2 × 2 × 2 × 2 × 3 × 3
144 = 2^{4} × 3^{2}
Step 2. Group the prime factors of 144 in pairs.
144 = 2^{2} × 2^{2} × 3^{2}
Step 3. Pick one factor from each pair and the square root of 144 can be written as:
√144 = √(2^{2} × 2^{2} × 3^{2})
√144 = √(2 × 2 × 3)^{2}
√144 = ((2 × 2 × 3)^{2})^{1/2} = ±(2 × 2 × 3)
√144 = ±12
Square Root of 144 by Long Division
Follow the steps shown below to find the square root of 144 by long division.
Step 1. Write 144 as shown in the figure. Start pairing the number in pairs of two digits from the right end by putting a bar on top of them. The unpaired number left in the left can be treated as a single entity as shown below. In the case of 144, 44 will be grouped under one bar and 1 under the second bar.
Step 2. Find a number which when multiplied by itself results in a number equal to or less than 1.
Step 3. Bring down the next pair of numbers. Here it is 44.
Multiply the quotient 1 by 2 (or add with itself) and write it as the new divisor’s ten’s place digit.
Step 4. Choose a number for the unit’s place of the divisor such that when it is multiplied with the new divisor, it will give 44 or a smaller number closest to 44.
Here the number is 22 as 22 × 2 = 44.
Explore square roots using illustrations and interactive examples.
Important Notes:
 The square root of 144 is represented as √144 in radical form and as (144)^{1/2} in exponential form.
 The square root of any number is both negative and positive for the same numerical value. The square root of 144 is +12 and 12.
 There will be n/2 digits in the square root of an even number with n digits.
 There will be (n+2)/2 digits in the square root of an odd number with n digits
Challenging Questions:
 Jason is running on a square ground with an area of 144 square feet. How much more he would have to run if later he wants to run on a square ground of area 441 square feet?
Square Root of 144 Solved Examples

Example 1: Zack wants to find the square root of 49/144. Can you help Zack?
Solution:
Prime factorization of 49 = 7 × 7
Prime factorization of 144: 2^{4} × 3^{2}Hence, the square root of 49/144 = √49/√144
= √(7 × 7)/√(2^{4} × 3^{2})
= 7/12 
Example 2: Find the square root of 144 by repeated subtraction method?
Solution:
 144  1 = 143
 143  3 = 140
 140  5 = 135
 135  7 = 128
 128  9 = 119
 119  11 = 108
 108  13 = 95
 95  15 = 80
 80  17 = 63
 63  19 = 44
 44  21 = 23
 23  23 = 0
So, starting from 144, we have subtracted 12 times to get 0.
Thus the square root of 144 is 12.
FAQs on Square Roots of 144
Is the square root of 144 is a rational number?
Yes, the square root of 144 is a rational number.
The square roots of 144 are 12 and 12 which are rational numbers.
What is the prime factorization of 144?
Prime factorization of 144: 2^{4} × 3^{2}
What different methods can be used to find the square root of 144?
We can find the square root of 144 by the following methods:
 Long division method
 Prime factorization
 Repeated subtraction method
What is the square root of 144?
The square root of negative numbers is imaginary.
It is represented as √144 = 12i.
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