123 LearnersLast updated on May 26th, 2025
Square Root of 2344
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 fields like vehicle design, finance, etc. Here, we will discuss the square root of 2344.
What is the Square Root of 2344?
The square root is the inverse of the square of the number. 2344 is not a perfect square. The square root of 2344 is expressed in both radical and exponential form. In the radical form, it is expressed as √2344, whereas in the exponential form it's expressed as (2344)^(1/2). √2344 ≈ 48.42, 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 2344
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 2344 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 2344 is broken down into its prime factors.
Step 1: Finding the prime factors of 2344 Breaking it down, we get 2 x 2 x 2 x 293: 2^3 x 293
Step 2: Now we found the prime factors of 2344. The second step is to make pairs of those prime factors. Since 2344 is not a perfect square, the digits of the number can’t be grouped in pairs.
Therefore, calculating √2344 using prime factorization is not straightforward.
Square Root of 2344 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, we need to group the numbers from right to left. In the case of 2344, we need to group it as 23 and 44.
Step 2: Now we need to find n whose square is less than or equal to 23. We can say n is 4 because 4 x 4 = 16, which is less than 23. The quotient is 4, and after subtracting 16 from 23, the remainder is 7.
Step 3: Bring down 44 to form the new dividend, which is 744. Add the old divisor (4) to itself (4 + 4 = 8) to form the new divisor.
Step 4: Find n such that 8n x n ≤ 744. Let n be 9, then 89 x 9 = 801, which is greater than 744, so we try n = 8, 88 x 8 = 704, which fits.
Step 5: Subtract 704 from 744, leaving a remainder of 40. The quotient is now 48.
Step 6: Since the remainder is less than the divisor, and we need more precision, add a decimal point and bring down 00, making it 4000.
Step 7: Find the new divisor by doubling the current quotient (48) to get 96. Find n such that 96n x n ≤ 4000. Try n = 4, then 964 x 4 = 3856.
Step 8: Subtract 3856 from 4000, leaving a remainder of 144. The quotient is 48.4.
Step 9: Continue these steps until the desired precision is reached.
The approximation of √2344 is 48.42.
Square Root of 2344 by Approximation Method
Approximation is another method for finding 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 2344 using the approximation method.
Step 1: Identify the closest perfect squares to 2344. The smallest perfect square is 2304 (48^2) and the largest is 2401 (49^2). √2344 falls between 48 and 49.
Step 2: Apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square)
Using this formula, (2344 - 2304) / (2401 - 2304) = 40 / 97 ≈ 0.41.
Adding this to the closest lower square root, we get 48 + 0.41 = 48.41.
Thus, the square root of 2344 is approximately 48.41.
Common Mistakes and How to Avoid Them in the Square Root of 2344
Students often make mistakes while finding the square root, such as forgetting about the negative square root or skipping steps in the long division method. Let us look at a few common mistakes in detail.
Mistake 1
Forgetting about the negative square root
It is important to remember that a number has both positive and negative square roots. However, we often take only the positive square root, as it is the required one in many contexts.
For example, √2344 ≈ 48.42, but there is also -48.42, which should not be forgotten.
Mistake 2
Not adding the square root symbol in proper places
Improper use of the square root symbol is a common mistake. It is important to simplify numbers inside the square root before proceeding.
For example, √(12+24) ≠ √12 + √24. The correct way is √(12+24) = √36.
Mistake 3
Not finding the correct value of a non-perfect square
The first step is to simplify the numbers inside the square root to avoid mistakes while identifying the approximate value.
For example, √2344 ≠ 48, the correct approximation is √2344 ≈ 48.42.
Mistake 4
Confusing the square root symbol with the cube root
Students should understand the difference between cube root and square root.
For example, √2344 and ∛2344 are different.
Mistake 5
Making mistakes in long division
Finding a square root using the long division method involves many steps. Students might skip a step accidentally, leading to a wrong answer. This may occur during subtraction or elsewhere in the process.
Square root of 2344 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √2344?
The area of the square is 2344 square units.
Explanation
The area of the square = side^2.
The side length is given as √2344.
Area of the square = (√2344) x (√2344) = 2344.
Therefore, the area of the square box is 2344 square units.
Problem 2
A square-shaped building measuring 2344 square feet is built; if each of the sides is √2344, what will be the square feet of half of the building?
1172 square feet
Explanation
To find half of the building's area, divide the total area by 2.
Dividing 2344 by 2 = 1172.
So half of the building measures 1172 square feet.
Problem 3
Calculate √2344 x 5.
242.1
Explanation
The first step is to find the square root of 2344, which is approximately 48.42.
Then multiply 48.42 by 5.
So, 48.42 x 5 = 242.1.
Problem 4
What will be the square root of (2304 + 40)?
The square root is 48.
Explanation
To find the square root, we need to find the sum of (2304 + 40).
2304 + 40 = 2344, and then √2344 ≈ 48.
Therefore, the square root of (2304 + 40) is approximately ±48.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √2344 units and the width ‘w’ is 38 units.
We find the perimeter of the rectangle as 172.84 units.
Explanation
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√2344 + 38) ≈ 2 × (48.42 + 38) = 2 × 86.42 = 172.84 units.
FAQ on Square Root of 2344
1.What is √2344 in its simplest form?
2.Mention the factors of 2344.
3.Calculate the square of 2344.
4.Is 2344 a prime number?
5.2344 is divisible by?
6.How does learning Algebra help students in Qatar make better decisions in daily life?
7.How can cultural or local activities in Qatar support learning Algebra topics such as Square Root of 2344?
8.How do technology and digital tools in Qatar support learning Algebra and Square Root of 2344?
9.Does learning Algebra support future career opportunities for students in Qatar?
Important Glossaries for the Square Root of 2344
- 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, which is √16 = 4.
- Irrational number: An irrational number is a number that cannot be written in the form of p/q, 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 usually the positive square root that is used in practical applications. This is called the principal square root.
- Prime factorization: The expression of a number as the product of its prime factors. For example, 2344 = 2 x 2 x 2 x 293.
- Long division method: A step-by-step division process used to find the square root of a number, particularly useful for non-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.
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