129 LearnersLast updated on May 26th, 2025
Square Root of 2744
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 such as vehicle design, finance, etc. Here, we will discuss the square root of 2744.
What is the Square Root of 2744?
The square root is the inverse of squaring a number. 2744 is a perfect square. The square root of 2744 is expressed in both radical and exponential forms. In radical form, it is expressed as √2744, whereas (2744)^(1/2) in exponential form. √2744 = 52, which is a rational number because it can be expressed as a fraction of integers.
Finding the Square Root of 2744
The prime factorization method is used for perfect square numbers. Let us now learn the methods for finding the square root of 2744:
- Prime factorization method
- Long division method
- Verification method
Square Root of 2744 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now, let us look at how 2744 is broken down into its prime factors.
Step 1: Finding the prime factors of 2744 Breaking it down, we get 2 × 2 × 2 × 7 × 7 × 7 × 7: 2^3 × 7^4
Step 2: Now we found the prime factors of 2744. The second step is to make pairs of those prime factors. Since 2744 is a perfect square, we can pair the factors: (2 × 2) and (7 × 7) × (7 × 7)
Step 3: The square root of 2744 is the product of the numbers in each pair: √2744 = 2 × 7 × 7 = 52
Square Root of 2744 by Long Division Method
The long division method is used for perfect and non-perfect square numbers. Here is how to find the square root of 2744 using the long division method, step by step.
Step 1: To begin with, pair the digits of 2744 from right to left as 27 and 44.
Step 2: Find a number whose square is less than or equal to the first pair, 27. That number is 5 because 5^2 = 25.
Step 3: Subtract 25 from 27, leaving a remainder of 2. Bring down the next pair, 44, to make it 244.
Step 4: Double the divisor (5) and place it as 10 to form a new divisor. Find a digit x such that 10x × x is less than or equal to 244.
Step 5: The number x is 2 because 102 × 2 = 204. Subtract 204 from 244 to get 40.
Step 6: Bring down pairs of zeros and continue the process until you reach the desired accuracy.
The square root of 2744 is 52.
Verification of the Square Root of 2744
Verification is a simple method to confirm the calculated square root.
Multiply 52 by itself: 52 × 52 = 2704 + 40 = 2744
Thus, the square root of 2744 is confirmed as 52.
Common Mistakes and How to Avoid Them in the Square Root of 2744
Students may make mistakes while finding the square root, such as not recognizing the perfect square or using incorrect methods. Let's explore some common mistakes in detail.
Mistake 1
Ignoring the Negative Square Root
It's essential to remember that a number has both positive and negative square roots. However, we often consider only the positive square root, as it's the principal value.
For example, √2744 = 52, but there's also -52, which should not be overlooked.
Mistake 2
Incorrect Pairing of Digits
Incorrectly pairing digits during the long division method can lead to errors. Ensure that digits are correctly paired from right to left for accurate calculations.
Mistake 3
Using Wrong Prime Factors
Mistakes can occur if incorrect prime factors are used. Always verify your prime factorization to ensure accuracy.
For example, √2744 = √(2^3 × 7^4) is correct, while √(2 × 7^6) is incorrect.
Mistake 4
Confusing Square Root with Cube Root
It's important to distinguish between square roots and cube roots, as they are different operations. Ensure students understand the difference, e.g., √2744 and ∛2744 are not the same.
Mistake 5
Errors in Long Division Steps
The long division method involves multiple steps, and skipping any can lead to incorrect results. Practice the method thoroughly to avoid such errors.
Square Root of 2744 Examples
Problem 1
Can you help Emma find the area of a square box if its side length is given as √2744?
The area of the square is 2704 square units.
Explanation
The area of the square = side^2.
The side length is given as √2744.
Area of the square = side^2
= √2744 × √2744
= 52 × 52 = 2704.
Therefore, the area of the square box is 2704 square units.
Problem 2
A square-shaped garden measuring 2744 square feet is built; if each of the sides is √2744, what will be the square feet of half of the garden?
1372 square feet.
Explanation
We can divide the given area by 2, as the garden is square-shaped.
Dividing 2744 by 2, we get 1372.
So half of the garden measures 1372 square feet.
Problem 3
Calculate √2744 × 3.
156
Explanation
The first step is to find the square root of 2744, which is 52.
The second step is to multiply 52 by 3.
So, 52 × 3 = 156.
Problem 4
What will be the square root of (2744 + 56)?
The square root is approximately 53.
Explanation
To find the square root, first find the sum of (2744 + 56).
2744 + 56 = 2800.
Then, √2800 is approximately 52.9.
Therefore, the square root of (2744 + 56) is approximately ±53.
Problem 5
Find the perimeter of a rectangle if its length ‘l’ is √2744 units and the width ‘w’ is 38 units.
The perimeter of the rectangle is 180 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√2744 + 38)
= 2 × (52 + 38)
= 2 × 90
= 180 units.
FAQ on Square Root of 2744
1.What is √2744 in its simplest form?
2.What are the factors of 2744?
3.Calculate the square of 52.
4.Is 2744 a prime number?
5.What numbers is 2744 divisible by?
6.How does learning Algebra help students in Indonesia make better decisions in daily life?
7.How can cultural or local activities in Indonesia support learning Algebra topics such as Square Root of 2744?
8.How do technology and digital tools in Indonesia support learning Algebra and Square Root of 2744?
9.Does learning Algebra support future career opportunities for students in Indonesia?
Important Glossaries for the Square Root of 2744
- Square root: A square root is the inverse of squaring a number. Example: 4^2 = 16, and the inverse of squaring is the square root, √16 = 4.
- Perfect square: A number that is the square of an integer. For example, 2744 is a perfect square because √2744 = 52, an integer.
- Rational number: A number that can be expressed as a fraction of two integers, where the denominator is not zero. Example: √4 = 2, which is a rational number.
- Exponentiation: The process of raising a number to a power. Example: 2^3 = 8.
- Long division: A method used to divide numbers and find square roots, especially for larger numbers.
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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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