113 LearnersLast updated on May 26th, 2025
Square Root of 3104
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 fields of engineering, finance, etc. Here, we will discuss the square root of 3104.
What is the Square Root of 3104?
The square root is the inverse of the square of the number. 3104 is not a perfect square. The square root of 3104 is expressed in both radical and exponential form. In radical form, it is expressed as √3104, whereas in exponential form it is (3104)^(1/2). √3104 ≈ 55.689, 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 3104
The prime factorization method is used for perfect square numbers. However, the prime factorization method is not used for non-perfect square numbers where long-division and approximation methods are used. Let us now learn the following methods:
- Prime factorization method
- Long division method
- Approximation method
Square Root of 3104 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 3104 is broken down into its prime factors.
Step 1: Finding the prime factors of 3104. Breaking it down, we get 2 x 2 x 2 x 2 x 2 x 97 = 2^5 x 97.
Step 2: Now we found out the prime factors of 3104. The second step is to make pairs of those prime factors. Since 3104 is not a perfect square, the digits of the number can’t be grouped in pairs. Therefore, calculating √3104 using prime factorization is not straightforward.
Square Root of 3104 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 3104, we need to group it as 04 and 31.
Step 2: Now we need to find n whose square is ≤ 31. We can say n is ‘5’ because 5 x 5 = 25, which is less than 31. Now the quotient is 5, and subtracting gives a remainder of 6.
Step 3: Bring down 04, making it the new dividend of 604. Add the old divisor with the same number: 5 + 5 = 10, which will be our new divisor.
Step 4: The new divisor will be 10n. Now we need to find n such that 10n x n ≤ 604. Let’s consider n as 5, so 105 x 5 = 525.
Step 5: Subtract 525 from 604, the difference is 79, and the quotient is 55.
Step 6: Since the dividend is less than the divisor, we need to add a decimal point. Adding the decimal point allows us to add two zeroes to the dividend. Now the new dividend is 7900.
Step 7: Now we need to find the new divisor. Let’s choose 7 because 1117 x 7 = 7819.
Step 8: Subtracting 7819 from 7900 gives a remainder of 81.
Step 9: Now the quotient is 55.7. Continue doing these steps until we get more decimal places or the remainder is zero. So the square root of √3104 is approximately 55.689.
Square Root of 3104 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 3104 using the approximation method.
Step 1: Now we have to find the closest perfect squares of √3104. The smallest perfect square less than 3104 is 3025, and the largest perfect square greater than 3104 is 3136. √3104 falls somewhere between 55 and 56.
Step 2: Now we need to apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Using the formula (3104 - 3025) / (3136 - 3025) = 79 / 111 ≈ 0.7126. Adding this decimal to the lower integer: 55 + 0.7126 = 55.7126. Therefore, the square root of 3104 is approximately 55.7126.
Common Mistakes and How to Avoid Them in the Square Root of 3104
Students do make mistakes while finding the square root, such as forgetting about the negative square root. Skipping long division steps, 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 often consider only the positive square root, as it is the required one in most contexts.
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 before moving to the next step.
For example: √(12 + 24) = √12 + √24 is incorrect. The correct way 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 incorrect; the correct approach 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 avoid 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, resulting in a wrong answer at the end of the sum. This may either happen in subtracting or elsewhere.
Square root of 3104 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √3104?
The area of the square is approximately 9647.521 square units.
Explanation
The area of the square = side².
The side length is given as √3104.
Area of the square = side² = √3104 × √3104 = 3104.
Therefore, the area of the square box is approximately 9647.521 square units.
Problem 2
A square-shaped building measuring 3104 square feet is built; if each of the sides is √3104, what will be the square feet of half of the building?
1552 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 3104 by 2 = we get 1552.
So half of the building measures 1552 square feet.
Problem 3
Calculate √3104 x 5.
278.445
Explanation
The first step is to find the square root of 3104, which is approximately 55.689.
The second step is to multiply 55.689 by 5. So 55.689 × 5 ≈ 278.445.
Problem 4
What will be the square root of (3100 + 4)?
The square root is 56.
Explanation
To find the square root, we need to find the sum of (3100 + 4).
3100 + 4 = 3104, and then √3104 ≈ 55.689.
Therefore, the square root of (3100 + 4) is approximately ±55.689.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √3104 units and the width ‘w’ is 20 units.
We find the perimeter of the rectangle as approximately 151.378 units.
Explanation
Perimeter of the rectangle = 2 × (length + width). Perimeter = 2 × (√3104 + 20) = 2 × (55.689 + 20) = 2 × 75.689 ≈ 151.378 units.
FAQ on Square Root of 3104
1.What is √3104 in its simplest form?
2.Mention the factors of 3104.
3.Calculate the square of 3104.
4.Is 3104 a prime number?
5.3104 is divisible by?
6.How does learning Algebra help students in Canada make better decisions in daily life?
7.How can cultural or local activities in Canada support learning Algebra topics such as Square Root of 3104?
8.How do technology and digital tools in Canada support learning Algebra and Square Root of 3104?
9.Does learning Algebra support future career opportunities for students in Canada?
Important Glossaries for the Square Root of 3104
- Square root: A square root is the inverse of a square. Example: 4^2 = 16 and the inverse of the square is the square root, that is √16 = 4.
- 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.
- Long division method: A method used to find the square root of a number, especially when the number is not a perfect square.
- Prime factorization: Breaking down a number into its basic prime factors. For example, the prime factorization of 3104 is 2^5 × 97.
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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.
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