Square Root of 121 is 11. It is represented as √(121) or (121)1/2. Square Root of a number is defined as the number that when multiplied by itself gives the original number. When multiplied by itself, √(121) will result in the number 121. Hence, the value of the square root of 121 is 11.
Also, (-11) × (-11) = 121. So, we say that -11 is also the square root of 121.
In this article, we will learn What is Value of Square Root of 121, and How to Find Value of Square Root of 121.
What is Square Root of 121?
Square root of 121 is denoted as √121. It is a rational number, meaning it results in a perfect square. When we talk about the square root of 121, we’re looking for a number that, when multiplied by itself, gives us the number 121 i.e., 11 as 11 × 11 = 121.
Square Root of 121 is given as:
√121 = 11 × 11
Square Root of 121 Calculator
Try out the following calculator to find out square root of 121
Value of Root of 121
Numerical value of square root 121 is 11 which means 121 is a perfect square.
√121 = √112= 11
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How to Find Square Root of 121?
Square root of a number is a value that, when you multiply it by itself, you get the original number. To find the square root, first, see if the number is a perfect square, which means its root is a whole number. It’s easier to figure out the square root of a perfect square than a number that’s not perfect.
Note: 121 is a Perfect Square
There are three methods to find Square root of 121,
- Long Division Method
- Prime Factorization Method
- Repeated Subtraction Method
Let’s learn about these method in detail one by one.
Square Root of 121 by Long Division Method
To find square root of any number using Long Division, we can use the following steps:
Step 1: Group digits in pairs from the decimal point (if any) to the left and right.
Step 2: Find a number which is more suitable for the division or the number Whose Square is Less Than or Equal to the Original number.
Step 3: Subtract the perfect square from the first group of digits.
Step 4: Write down the next pair of digits.
Step 5: Double the current answer and find a digit to place next to it that, when multiplied by the new number, is less than or equal to the current number.
Step 6: Repeat steps 4-6 until desired accuracy is reached.
As We discussed earlier, 121 is a perfect square, So we get easily the square root by Long Division Method, Let’s discuss how we find it in the following steps:
Step 1: We must first write 121 as 121.000000 to make it easier to divide.
Step 2: Now, Check whether 121 is perfect square or not, and we find yes 121 is a perfect square.
Step 3: If we found the perfect square, then simply get your answer as the square root of the number.
Read More about, Square Root by Long Division Method
Square Root 121 by Prime Factorization Method
In this method, we normally perform the prime factorization and pair the factors to find the square root value. If we get a pair of every number, then we must say that number is a perfect square.
Prime Factorization of 121
As we know, 121 is a perfect square.
Prime factor of 121 is,
121 = 11 × 11
So,
√(121) = 11
So, Square root of 121 is 11.
Square Root of 121 by Repeated Subtraction
As, 121 is a perfect square its square root is easily found using repeated subtraction methods, i.e.
121 – 1 = 120
120 – 3 = 117
117 – 5 = 112
112 – 7 = 105
105 – 9 = 96
96 – 11 = 85
85 – 13 = 72
72 – 15 = 57
57 – 17 = 40
40 – 19 = 21
21 – 21 = 0
As, 0 result is obtained in 11th step 11 is square root of 121
Trick For Finding Square Root of 121
Square root of 121 can be easily found by guessing nearest perfect square of that number and the steps for the same is,
Square Root of 121 by Guess and Check Method
In the Guess and Check method, we generally make a initial guess and then think it wisely and try to refine to get a number that is bit closer to the actual value.
Step 1: Begin by making an initial guess for the square root of the given number. As this depends on your understanding on perfect squares.
Step 2: Square your first guess, then multiply that number and check whether you find your number or not, If not then you need to move to next step , else you got your answer.
Step 3: If the result is too large, then you choose a large number you should think less than that number vice versa.
Step 4: We need to repeat the process until you get the original number.
Step 5: Once you got your special number for the original number, then you should check by multiplying by itself. Once you confirm, its sure that you had done a perfect approximation.
Now, Lets apply these steps for finding Square root of 121,
Step 1: Let’s start with the guess √121 = 11
Step 2: Check whether when we multiply by itself it gives original number or not as 11 × 11 = 121, so you got the original number
Step 3: So, you got square root of 121 by Guess and Check Method
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Square Root of 121 – FAQs
What is the Value of Square Root of 121?
The value of the square root of 121, is 11.
Is Square Root of 121 Rational or Irrational Number?
Square Root of 121 i.e., √121 is an rational number as it can be written as √121 = 11.
Is 121 a Perfect Square?
Yes, 121 is a perfect square as it can be written as 11 × 11.
Is the Square Root of 121 Negative?
Square root of 121 is 11, which is an positive integer or a natural number.
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