129 LearnersLast updated on May 26th, 2025
Square Root of 3121
If a number is multiplied by the same number, the result is a square. The inverse of the square is a square root. The square root is used in the field of vehicle design, finance, etc. Here, we will discuss the square root of 3121
What is the Square Root of 3121?
The square root is the inverse of the square of the number. 3121 is not a perfect square. The square root of 3121 is expressed in both radical and exponential form. In the radical form, it is expressed as √3121, whereas (3121)^(1/2) in the exponential form. √3121 ≈ 55.834, which is an irrational number because it cannot be expressed in the form of p/q, where p and q are integers and q ≠ 0.
Finding the Square Root of 3121
The prime factorization method is used for perfect square numbers. However, the prime factorization method is not used for non-perfect square numbers where the long-division method and approximation method are used. Let us now learn the following methods:
- Prime factorization method
- Long division method
- Approximation method
Square Root of 3121 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 3121 is broken down into its prime factors:
Step 1: Finding the prime factors of 3121 Breaking it down, we get 3121 = 7 × 11 × 41
Step 2: Now we found out the prime factors of 3121. The second step is to make pairs of those prime factors. Since 3121 is not a perfect square, therefore the digits of the number can’t be grouped in pairs. Therefore, calculating 3121 using prime factorization is impossible.
Square Root of 3121 by Long Division Method
The long division method is particularly used for non-perfect square numbers. In this method, we should check the closest perfect square number for the given number. Let us now learn how to find the square root using the long division method, step by step:
Step 1: To begin with, we need to group the numbers from right to left. In the case of 3121, we need to group it as 21 and 31.
Step 2: Now we need to find n whose square is less than or equal to 31. We can say n is 5 because 5 × 5 = 25 which is less than 31. Now the quotient is 5, and after subtracting 25 from 31, the remainder is 6.
Step 3: Bring down 21 which is the new dividend. Add the old divisor with the same number 5 + 5, we get 10 which will be our new divisor.
Step 4: The new divisor will be the sum of the previous quotient and divisor. Now we get 10n as the new divisor, we need to find the value of n.
Step 5: The next step is finding 10n × n ≤ 621. Let us consider n as 5, now 105 × 5 = 525.
Step 6: Subtract 621 from 525, the difference is 96, and the quotient is 55.
Step 7: Since the dividend is less than the divisor, we need to add a decimal point. Adding the decimal point allows us to add two zeros to the dividend. Now the new dividend is 9600.
Step 8: Now we need to find the new divisor that is 558 because 558 × 8 = 4464.
Step 9: Subtracting 4464 from 9600 we get the result 5136.
Step 10: Now the quotient is 55.8.
Step 11: Continue doing these steps until we get two numbers after the decimal point. Suppose if there are no decimal values, continue till the remainder is zero. So the square root of √3121 is approximately 55.83.
Square Root of 3121 by Approximation Method
The approximation method is another method for finding the square roots. It is an easy method to find the square root of a given number. Now let us learn how to find the square root of 3121 using the approximation method.
Step 1: Now we have to find the closest perfect square of √3121. The smallest perfect square less than 3121 is 3025 (55^2) and the largest perfect square greater than 3121 is 3136 (56^2). √3121 falls somewhere between 55 and 56.
Step 2: Now we need to apply the formula that is (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Going by the formula (3121 - 3025) / (3136 - 3025) = 96 / 111 ≈ 0.865. Using the formula, we identified the decimal point of our square root. The next step is adding the value we got initially to the decimal number which is 55 + 0.865 = 55.865, so the square root of 3121 is approximately 55.865.
Common Mistakes and How to Avoid Them in the Square Root of 3121
Students do make mistakes while finding the square root, likewise forgetting about the negative square root, skipping long division methods, etc. Now let us look at a few of those mistakes that students tend to make in detail.
Mistake 1
Forgetting about the negative square root
It is important to make students aware that a number does have both positive and negative square roots. However, we will be taking only the positive square root, as it is the required one.
For example, √50 = 7.07, there is also -7.07 which should not be forgotten.
Mistake 2
Not adding the square root symbol in proper places
Not using the square root properly is another mistake that children make. To resolve this, we need to teach children that simplifying the numbers inside the square root is important and then move on to the second step.
For example, √(12+24) = √12 + √24 is the wrong method of using roots. The right way of using roots is √(12+24) = √36.
Mistake 3
Not finding the correct value of a non-perfect square
The first step that needs to be taught to children is to simplify the numbers inside the square root. This is important so that students do not make mistakes while identifying the approximate value.
For example, √50 = 7 is wrong, the correct answer is √50 ≈ 7.071.
Mistake 4
Confusing the square root symbol with the cube root
Students need to be taught the difference between cube root and square root constantly as this will help them keep away from mistakes.
For example, √50 and ∛50 are different.
Mistake 5
Making mistakes in long division
Finding a square root using the long division method involves many steps. Due to this, many students might skip a step accidentally which results in a wrong answer at the end of the sum. This may either happen in subtracting or elsewhere.
Square Root of 3121 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √2500?
The area of the square is 2500 square units.
Explanation
The area of the square = side^2.
The side length is given as √2500.
Area of the square = side^2 = √2500 × √2500 = 50 × 50 = 2500.
Therefore, the area of the square box is 2500 square units.
Problem 2
A square-shaped building measuring 3121 square feet is built; if each of the sides is √3121, what will be the square feet of half of the building?
1560.5 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 3121 by 2 = we get 1560.5.
So half of the building measures 1560.5 square feet.
Problem 3
Calculate √3121 × 5.
Approximately 279.17
Explanation
The first step is to find the square root of 3121 which is approximately 55.834, the second step is to multiply 55.834 with 5. So 55.834 × 5 ≈ 279.17.
Problem 4
What will be the square root of (2500 + 21)?
The square root is approximately 50.21
Explanation
To find the square root, we need to find the sum of (2500 + 21).
2500 + 21 = 2521, and then 2521 ≈ 50.21.
Therefore, the square root of (2500 + 21) is approximately ±50.21.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √2500 units and the width ‘w’ is 38 units.
We find the perimeter of the rectangle as 176 units.
Explanation
Perimeter of the rectangle = 2 × (length + width). Perimeter = 2 × (√2500 + 38) = 2 × (50 + 38) = 2 × 88 = 176 units.
FAQ on Square Root of 3121
1.What is √3121 in its simplest form?
2.Mention the factors of 3121.
3.Calculate the square of 3121.
4.Is 3121 a prime number?
5.3121 is divisible by?
6.How does learning Algebra help students in Vietnam make better decisions in daily life?
7.How can cultural or local activities in Vietnam support learning Algebra topics such as Square Root of 3121?
8.How do technology and digital tools in Vietnam support learning Algebra and Square Root of 3121?
9.Does learning Algebra support future career opportunities for students in Vietnam?
Important Glossaries for the Square Root of 3121
- Square root: A square root is the inverse of a square. Example: 5^2 = 25 and the inverse of the square is the square root that is √25 = 5.
- Irrational number: An irrational number is a number that cannot be written in the form of p/q, where q is not equal to zero and p and q are integers.
- Principal square root: A number has both positive and negative square roots, however, it is always the positive square root that has more prominence due to its uses in the real world. That is the reason it is also known as a principal square root.
- Decimal: If a number has a whole number and a fraction in a single number then it is called a decimal. For example, 7.86, 8.65, and 9.42 are decimals.
- Perfect square: A perfect square is an integer that is the square of an integer. For example, 1, 4, 9, 16, and 25 are perfect squares.
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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.
Fun Fact
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