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 fields such as vehicle design, finance, etc. Here, we will discuss 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.
The prime factorization method is used for perfect square numbers. Let us now learn the methods for finding the square root of 2744:
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
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 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.
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.
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.
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.
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.
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.
Calculate √2744 × 3.
156
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.
What will be the square root of (2744 + 56)?
The square root is approximately 53.
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.
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.
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√2744 + 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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