Last updated on May 26th, 2025
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.
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.
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:
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.
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.
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.
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.
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.
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.
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.
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
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.
Calculate √2704 × 5.
260
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.
What will be the square root of (676 + 1028)?
The square root is 52.
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.
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.
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√2704 + 38)
= 2 × (52 + 38)
= 2 × 90
= 180 units.
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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