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Square Root

What Is the Square Root of 144? | How to Find the Square Root of 144?

Written by Prerit Jain

Updated on: 12 Aug 2023

What Is the Square Root of 144? | How to Find the Square Root of 144?

What Is the Square Root of 144? | How to Find the Square Root of 144?

The square root of 144 is 12. The inversion of subtraction is addition, and the inversion of multiplication is division in the same way the inversion of the square root of a value is squaring the number. The value of any number that when multiplied by itself gives the original number. The number 12 when they are squared 122 gives 144, and when the number is multiplied by itself 12×12 it gives the original value of 144. 

For any given number before finding its square root we must know whether the given number is a perfect square number or not. A perfect square number is one that when squared has a whole number and was easy to find. A non-perfect square number when squared has only integers and not a whole number and is found using the long division method. 

Methods to find the square root of 144

Since the number 144 is a perfect square and a rational number the square root can be found using three methods

  • Prime factorization method
  • Long division method
  • Repeated subtraction

Prime factorization method

Prime factorization is one of the easiest methods to find the square root of any number. Let us take n as the prime number, by grouping the similar numbers we get n2, by multiplying the similar n2. The value we get is the square root of the number. 
The prime factor of 144 = 12×12
By squaring them we get 122, since two is the only similar square we take the common one.
Here, the common square is 12.
Hence, the √144 = 12

Repeated subtraction method

For the repeated subtraction method we should start to multiply the given number with only odd numbers. The step in which zero is obtained is the square root of the given number.

  1. 144 – 1 = 143
  2. 143 – 3 = 140
  3. 140 – 5 = 135
  4. 135 – 7 = 128
  5. 128 – 9 = 119
  6. 119 – 11 = 108
  7. 108 – 13 = 95
  8. 95 – 15 = 80
  9. 80 – 17 = 63
  10. 63 – 19 = 44
  11. 44 – 21 = 23
  12. 23 – 23 = 0

Here, the value zero is obtained in the twelfth step.
Hence, the √144 = 12

Long division method

Long division is one of the easiest methods to find the square root of any number. It was the preferred method to be used for the non-perfect square numbers. Find the integer to divide the number and proceed with the long division. 

Long division method
Long division method

Hence, the √144 = 12

Solved examples

Q1: What is the sum of the square of 144 and the square root of 144?
A1: Square of 144 = 20736
The square root of 144 = 12
The sum of the square of 144 and the square root of 144 = 20736+12 = 20748

Q 2: Joel wants to find the square root value of √144/121 to help him solve the sum
A2: The √144 = 12.
The √121 = 11
Therefore, √144/121 = 12/11.

Q3: Help Sam solve the equation 6√144 – 1√144
A3: The √144 = 12.
Hence 6 (12) – 1 (12).
= 72-12
Hence by solving, we get 60.

Q4: What is the area of the square whose each side is equal to 12cm
A4: Area of the square = x2
Here x= 12
Therefore, 122 = 12 ×12 =144
Hence the area of the square with 12cm = 144 sq. cm

Frequently asked questions

What is the square root of 144?
The square root of 144 = 12.

Explain why the square root of 144 is a rational number
When finding the prime factor of 144 we get 122 which is entirely an even power hence all the numbers are positive integers which makes them rational numbers.

What is the value of 144 and the square root of 144?
The square root of 144 is 12,
144√144 = 144 ×12 = 1728

What is the real value for the square root of 144
The actual value for the 144 = 12

What is the square root of 1?
The square root of 1 = 1

What is the square root of (-144)?
The square root of minus digits is imaginary numbers or imaginary units which really don’t have a square root but the √-144 can be written as 12i.

Is 144 a perfect square number?
Yes, 144 is a perfect square number.

We hope that we have answered all your queries related to the square root of 144!

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Prerit Jain

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