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Square Root

What Is the Square Root of 121? How To Find the Square Root of 121?

Written by Prerit Jain

Updated on: 12 Aug 2023

What Is the Square Root of 121? How To Find the Square Root of 121?

What Is the Square Root of 121? How To Find the Square Root of 121?

The square root of 121 is 11. The square root of a number is determined as a value that when multiplied by itself gives the actual number. Let us look into the number 121 as an example itself. The square root of 121 is 11 and when 11 is multiplied by itself 112 (11×11) = 121. Hence when a number is multiplied by itself it gives the actual given value. 

Before finding the square root of any given number we should look into two things. The one thing is if the given number is a perfect square or not a perfect square number. The next one is if the given number is a rational or irrational number. If the number given is a perfect square and a rational method. Then finding the square root of a number is easy. 

Methods to find the square root of 121

Since the number 121 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

To find the square root of a number using the prime factorization method first know the prime factors of the numbers. Let us take n as a prime number, by grouping their squares we get n2 now multiply them we get the square root of the number. 

  • Step1: Find the prime factor for the given number
    • 121 = 11× 11
  • Step 2: Group similar factors.
    • 121 = 112
  • Step 3: Multiply the similar factors
    • In this case, there is only one number that is similar to a square.
    • Hence, √121 = 11.

Repeated subtraction method

To find the square root of a number using the repeated subtraction method. Subtract the given number with the odd numbers. Bring down the subtracted value and start subtracting with the next odd value. Keep subtracting until you reach zero. The step in which zero is attained is the square root of the number. 

  1. 121 – 1 = 120
  2. 120 – 3 = 117
  3. 117 – 5 = 112
  4. 112 – 7 = 105
  5. 105 -9 = 96
  6. 96 – 11 = 85
  7. 85 – 13 = 72
  8. 72 – 15 = 57
  9. 57 – 17 = 40
  10. 40 – 19 = 21
  11. 21-21 = 0

We get zero at the 11th step. 
Hence, √121 = 11.

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 that can divide the number and proceed with the long division. 

Long division method
Long division method

Hence, √121 = 11.

Solved examples

Q 1: The roots of – (121) and (121) are the same, what did you think?
A 1: The negative square has no real root.
121 has real roots while  – (121) has only imaginary roots.
Hence, they are not similar

Q 2: Robert wants to simply 121 to its simplest form, let’s help her.
A 2: 121 = 11 × 11
Hence the simplest form of  √121 = 11

Q 3: solve 2√121 + 1√121 
A 3: The √121 = 11
= 2 (11) + 1 (11)
= 22 + 11
Hence by solving we get 33

Q 4: what is the value of x, if x√121 = 44
A 4: x√121 = 44
√121 = 11
Hence, x 11 = 44
X = 44/11 = 4
Therefore x = 4.

Q 5: Find the perimeter of the square if the area of the square tile is 121.
A 5: The area of the tile = √area = √121 = 11
The square tile has 4 sides therefore we multiply it by 4 = 4 ×11 = 44
Therefore the perimeter of the tile  = is 44 units.

Frequently asked question

What is the square root of 121?
The √121 = 11.

Is 121 a rational number?
Yes, 121 is a rational number because when we divide the number we get 11 and not 0 (p/q≠ 0)

What is a perfect square number?
A perfect square number is one when we find the root of the number we get a whole number and not a decimal. √121 = 11 hence 121 is a perfect square number. 

Manu bought 121 saplings, and he decided to plant them with the same number in rows and columns, how could he do that?
If Manu decides to plant equal numbers in both rows and columns then he must have squared them to find how much he should plant for them to be equal.
√121 = 11
Therefore, Manu planted 11 plants in each row and column.

What is the square root of 49?
The square root of 49 = 7.

How to find the square root for irrational numbers?
To find the square root for irrational numbers use the long division method

What is the square root of 36?
The square of 36:
√36 = 6

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Prerit Jain

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