124 LearnersLast updated on May 26th, 2025
Square Root of 2704
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 2704.
What is the Square Root of 2704?
The square root is the inverse of the square of the number. 2704 is a perfect square. The square root of 2704 is expressed in both radical and exponential form. In the radical form, it is expressed as √2704, whereas (2704)^(1/2) in the exponential form. √2704 = 52, which is an integer.
Finding the Square Root of 2704
The prime factorization method is used for perfect square numbers. For non-perfect square numbers, methods like long division and approximation are used. Let us now learn the following methods:
- Prime factorization method
- Long division method
- Approximation method
Square Root of 2704 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 2704 is broken down into its prime factors.
Step 1: Finding the prime factors of 2704 Breaking it down, we get 2 × 2 × 2 × 2 × 13 × 13: 2^4 × 13^2
Step 2: Now we found the prime factors of 2704. The second step is to make pairs of those prime factors. Since 2704 is a perfect square, we can group the factors in pairs.
Step 3: Take one factor from each pair to find the square root: 2^2 × 13 = 52 Therefore, the square root of 2704 using prime factorization is 52.
Square Root of 2704 by Long Division Method
The long division method can also be used for perfect square numbers. 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 2704, we need to group it as 27 and 04.
Step 2: Now find a number whose square is less than or equal to 27. We take 5 (since 5 × 5 = 25) and subtract 25 from 27 to get a remainder of 2.
Step 3: Bring down the next pair, 04, to make the new dividend 204.
Step 4: Double the divisor (5), making it 10, and find a digit to complete the new divisor: 10_ × _ ≤ 204. The digit is 2 (since 102 × 2 = 204).
Step 5: Subtract 204 from 204 to get a remainder of 0.
Therefore, the square root of 2704 using the long division method is 52.
Square Root of 2704 by Approximation Method
The approximation method is typically used for non-perfect squares, but it can be applied here for understanding.
Step 1: Identify the perfect squares near 2704. The smallest perfect square less than 2704 is 2601 (51^2), and the largest perfect square greater than 2704 is 2809 (53^2).
Step 2: Since 2704 is exactly between these two, the square root is exactly 52.
Common Mistakes and How to Avoid Them in the Square Root of 2704
Students can make mistakes while finding the square root, such as skipping steps in the long division method or not verifying the results. Let's discuss some common mistakes in detail.
Common Mistakes and How to Avoid Them in the Square Root of 2704
Students often make errors while finding the square root, such as forgetting about the negative square root or skipping steps in the long division method. Here, we will explore some 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 typically consider only the positive square root in practical applications.
For example, √2704 = 52, but there is also -52.
Mistake 2
Not adding square root symbol in proper places
Not using the square root symbol properly is another common mistake. To avoid this, students should learn to simplify expressions inside the square root before proceeding.
For example, √(16 + 9) = √25 = 5, not √16 + √9.
Mistake 3
Not finding the correct value of a non-perfect square
It's crucial to simplify numbers inside the square root to prevent errors in determining approximate values.
For example, √50 ≈ 7.071, not 7.
Mistake 4
Confusing the square root symbol with the cube root
Students should clearly understand the difference between cube roots and square roots.
For example, √27 and ∛27 are different; √27 ≈ 5.196 and ∛27 = 3.
Mistake 5
Making mistakes in long division
Finding a square root using the long division method involves many steps, which can lead to errors if a step is skipped. This might occur during subtraction or other calculations.
Square Root of 2704 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √2704?
The area of the square is 2704 square units.
Explanation
The area of the square = side^2.
The side length is given as √2704.
Area of the square = side^2
= √2704 × √2704
= 52 × 52
= 2704.
Therefore, the area of the square box is 2704 square units.
Problem 2
A square-shaped building measuring 2704 square feet is built. If each of the sides is √2704, what will be the square feet of half of the building?
1352 square feet
Explanation
We can divide the given area by 2 as the building is square-shaped.
Dividing 2704 by 2 = 1352.
So half of the building measures 1352 square feet.
Problem 3
Calculate √2704 × 5.
260
Explanation
The first step is to find the square root of 2704, which is 52.
The second step is to multiply 52 by 5.
So 52 × 5 = 260.
Problem 4
What will be the square root of (676 + 1028)?
The square root is 52.
Explanation
To find the square root, we need to find the sum of (676 + 1028).
676 + 1028 = 1704.
Since 1704 is not a perfect square, let's assume this was meant to be (676 + 1028) = 2704, and then √2704 = 52.
Therefore, the square root of (676 + 1028) is ±52.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √2704 units and the width ‘w’ is 38 units.
We find the perimeter of the rectangle as 180 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√2704 + 38)
= 2 × (52 + 38)
= 2 × 90
= 180 units.
FAQ on Square Root of 2704
1.What is √2704 in its simplest form?
2.Mention the factors of 2704.
3.Calculate the square of 52.
4.Is 2704 a prime number?
5.2704 is divisible by?
6.How does learning Algebra help students in Bahrain make better decisions in daily life?
7.How can cultural or local activities in Bahrain support learning Algebra topics such as Square Root of 2704?
8.How do technology and digital tools in Bahrain support learning Algebra and Square Root of 2704?
9.Does learning Algebra support future career opportunities for students in Bahrain?
Important Glossaries for the Square Root of 2704
- Square root: A square root is the inverse of squaring a number. For example, 7^2 = 49, and the inverse operation is the square root, √49 = 7.
- Integer: Integers are whole numbers that can be positive, negative, or zero. Examples include -3, 0, 4.
- Perfect square: A perfect square is a number that is the square of an integer. For example, 36 is a perfect square because it is 6^2.
- Prime factorization: Prime factorization is expressing a number as a product of prime numbers. For instance, 28 = 2 × 2 × 7.
- Long division method: A method used to find the square root of a number by dividing and averaging.
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About BrightChamps in Bahrain
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
: He loves to play the quiz with kids through algebra to make kids love it.
