126 LearnersLast updated on May 26th, 2025
Square Root of 7744
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 7744.
What is the Square Root of 7744?
The square root is the inverse of the square of the number. 7744 is a perfect square. The square root of 7744 is expressed in both radical and exponential form. In the radical form, it is expressed as √7744, whereas (7744)^(1/2) in the exponential form. √7744 = 88, which is a rational number because it can be expressed in the form of p/q, where p and q are integers and q ≠ 0.
Finding the Square Root of 7744
The prime factorization method is used for perfect square numbers. However, the long division method can also be used for any number. Let us now learn the following methods:
- Prime factorization method
- Long division method
Square Root of 7744 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 7744 is broken down into its prime factors.
Step 1: Finding the prime factors of 7744 Breaking it down, we get 2 x 2 x 2 x 2 x 11 x 11: 2^4 x 11^2
Step 2: Now we found out the prime factors of 7744. The second step is to make pairs of those prime factors. Since 7744 is a perfect square, we can pair the digits: (2 x 2) x (2 x 2) x (11 x 11).
Step 3: Taking one factor from each pair gives us the square root: 2 x 2 x 11 = 44.
Square Root of 7744 by Long Division Method
The long division method is particularly used for non-perfect square numbers, but it can also be used for perfect squares. 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 7744, we group it as 77 and 44.
Step 2: Now we need to find a number whose square is less than or equal to 77. We can use 8 since 8 x 8 = 64. Subtracting 64 from 77 gives us 13.
Step 3: Bring down the next pair, 44, making the new dividend 1344. Add the old divisor with the same number: 8 + 8 = 16, which will be our new divisor.
Step 4: The new divisor will be 160. Find a number n such that (160 + n) x n ≤ 1344. We find n = 8 since 168 x 8 = 1344.
Step 5: Subtracting 1344 from 1344 gives 0. So we have found the square root to be 88.
Common Mistakes and How to Avoid Them in the Square Root of 7744
Students do make mistakes while finding the square root, like forgetting about the negative square root, skipping steps in the long division method, etc. Now let us look at a few of those mistakes that students tend to make in detail.
Common Mistakes and How to Avoid Them in the Square Root of 7744
Students do make mistakes while finding the square root, like forgetting about the negative square root, skipping steps in the long division method, etc. Now let us look at a few of those mistakes that students tend to make in detail.
Mistake 1
Forgetting about the negative square root
It is important to make students aware that a number does have both positive and negative square roots. However, we will often consider only the positive square root in practical applications.
For example, √7744 = 88, but there is also -88.
Square Root of 7744 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √7744?
The area of the square is 7744 square units.
Explanation
The area of the square = side^2. The side length is given as √7744. Area of the square = side^2 = √7744 x √7744 = 88 x 88 = 7744. Therefore, the area of the square box is 7744 square units.
Problem 2
A square-shaped building measuring 7744 square feet is built; if each of the sides is √7744, what will be the square feet of half of the building?
3872 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped. Dividing 7744 by 2, we get 3872. So half of the building measures 3872 square feet.
Problem 3
Calculate √7744 x 5.
440
Explanation
The first step is to find the square root of 7744, which is 88. The second step is to multiply 88 by 5. So, 88 x 5 = 440.
Problem 4
What will be the square root of (7744 + 256)?
The square root is 92.
Explanation
To find the square root, we need to find the sum of (7744 + 256). 7744 + 256 = 8000. The square root of 8000 is 89.44, which can be approximated to 92 when rounded.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √7744 units and the width ‘w’ is 88 units.
352 units
Explanation
Perimeter of the rectangle = 2 × (length + width). Perimeter = 2 × (√7744 + 88) = 2 × (88 + 88) = 2 × 176 = 352 units.
FAQ on Square Root of 7744
1.What is √7744 in its simplest form?
2.Mention the factors of 7744.
3.Calculate the square of 88.
4.Is 7744 a perfect square?
5.7744 is divisible by?
Important Glossaries for the Square Root of 7744
- Square root: A square root is the inverse of a square. For example, 88^2 = 7744, and the inverse of the square is the square root, which is √7744 = 88.
- Perfect square: A perfect square is an integer that is the square of an integer. For example, 7744 is a perfect square because it is 88 squared.
- Rational number: A rational number is a number that can be expressed in the form of p/q, where q is not equal to zero and p and q are integers.
- Principal square root: A number has both positive and negative square roots, but the positive square root is often used in practical applications. This is known as the principal square root.
- Prime factorization: Prime factorization is expressing a number as the product of its prime factors. For example, the prime factorization of 7744 is 2^4 x 11^2.
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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
: He loves to play the quiz with kids through algebra to make kids love it.
