125 LearnersLast updated on May 26th, 2025
Square Root of 8281
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 8281.
What is the Square Root of 8281?
The square root is the inverse of the square of the number. 8281 is a perfect square. The square root of 8281 is expressed in both radical and exponential form. In the radical form, it is expressed as √8281, whereas (8281)^(1/2) in the exponential form. √8281 = 91, 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 8281
The prime factorization method is used for perfect square numbers. For non-perfect square numbers, the long division method and approximation method are used. Since 8281 is a perfect square, we will use the prime factorization method. Let us now learn the following methods:
- Prime factorization method
- Long division method
- Approximation method
Square Root of 8281 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 8281 is broken down into its prime factors.
Step 1: Finding the prime factors of 8281 Breaking it down, we get 91 x 91 = 8281. 91 is a product of 7 and 13, so the prime factorization of 8281 is 7 x 13 x 7 x 13.
Step 2: Now we found out the prime factors of 8281. The second step is to make pairs of those prime factors. Since 8281 is a perfect square, the digits of the number can be grouped in pairs. Therefore, √8281 = 7 x 13 = 91.
Square Root of 8281 by Long Division Method
The long division method is another way to find the square root of a number. 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 8281, we group it as 82 and 81.
Step 2: Now we need to find n whose square is closest to 82. We can say n as '9' because 9 x 9 = 81, which is less than or equal to 82. Now the quotient is 9 after subtracting 81 from 82. The remainder is 1.
Step 3: Now let us bring down 81, making the new dividend 181. Add the old divisor with the same number 9 + 9 = 18, which will be our new divisor.
Step 4: The new divisor will be the sum of the dividend and quotient. Now we get 18n as the new divisor, and we need to find the value of n.
Step 5: The next step is finding 18n x n ≤ 181. Let us consider n as 1, now 18 x 1 x 1 = 18.
Step 6: Subtract 181 from 18, and the difference is 163. The quotient is 91.
Step 7: Since 8281 is a perfect square, continuing the steps will yield 0 as the remainder, confirming that the square root of 8281 is 91.
Square Root of 8281 by Approximation Method
The approximation method is another method for finding square roots, and it is an easy method to find the square root of a given number. However, since 8281 is a perfect square, we can directly determine that the square root is 91.
Important Glossaries for the Square Root of 8281
Square root: A square root is the inverse of a square. Example: 9^2 = 81, and the inverse of the square is the square root, which is √81 = 9.
Rational number: A rational number is a number that can be written in the form of p/q, where q is not equal to zero, and p and q are integers. Perfect square: A perfect square is a number that is the square of an integer. For example, 81 is a perfect square because it is 9^2. Prime factorization: Breaking down a number into its prime factors. For example, the prime factorization of 28 is 2 x 2 x 7. Integer: An integer is a whole number that can be positive, negative, or zero. Examples include -3, 0, and 4.
Common Mistakes and How to Avoid Them in the Square Root of 8281
Students do make mistakes while finding the square root, such as forgetting about the negative square root or skipping steps in the long division method. 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 has both positive and negative square roots. However, we will be taking only the positive square root, as it is the required one. For example: √81 = 9, there is also -9 which should not be forgotten.
Mistake 2
Not adding square root symbol in proper places
Not using the square root properly is another mistake that children make. To resolve this, we need to teach children that simplifying the numbers inside the square root is important and then move on to the second step. For example: √(9+16) = √25 = 5, not √9 + √16 = 3 + 4.
Mistake 3
Not finding the correct value of a non-perfect square
The first step that needs to be taught to children is to simplify the numbers inside the square root. This is important so that students do not make mistakes while identifying the approximate value. For example: √50 ≈ 7.071, not 7.
Mistake 4
Confusing the square root symbol with the cube root
Students need to be taught the difference between cube root and square root constantly, as this will help them keep away from mistakes. For example: √27 and ∛27 are different.
Mistake 5
Making mistakes in long division
Finding a square root using the Long Division method involves many steps. Due to this, many students might skip a step accidentally, which results in a wrong answer at the end of the sum. This may either happen in subtraction or elsewhere.
Square root of 8281 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √8281?
The area of the square is 8281 square units.
Explanation
The area of the square = side^2. The side length is given as √8281. Area of the square = side^2 = √8281 x √8281 = 91 x 91 = 8281. Therefore, the area of the square box is 8281 square units.
Problem 2
A square-shaped building measuring 8281 square feet is built; if each of the sides is √8281, what will be the square feet of half of the building?
4140.5 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped. Dividing 8281 by 2 = we get 4140.5. So half of the building measures 4140.5 square feet.
Problem 3
Calculate √8281 x 5.
455
Explanation
The first step is to find the square root of 8281, which is 91. The second step is to multiply 91 with 5. So 91 x 5 = 455.
Problem 4
What will be the square root of (8281 + 19)?
The square root is 92.
Explanation
To find the square root, we need to find the sum of (8281 + 19). 8281 + 19 = 8300, and then √8300 ≈ 91.108. Therefore, the approximate square root of (8281 + 19) is ±91.108.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √8281 units and the width ‘w’ is 38 units.
We find the perimeter of the rectangle as 258 units.
Explanation
Perimeter of the rectangle = 2 × (length + width). Perimeter = 2 × (√8281 + 38) = 2 × (91 + 38) = 2 × 129 = 258 units.
FAQ on Square Root of 8281
1.What is √8281 in its simplest form?
2.Mention the factors of 8281.
3.Calculate the square of 8281.
4.Is 8281 a prime number?
5.8281 is divisible by?
6.How does learning Algebra help students in United Kingdom make better decisions in daily life?
7.How can cultural or local activities in United Kingdom support learning Algebra topics such as Square Root of 8281?
8.How do technology and digital tools in United Kingdom support learning Algebra and Square Root of 8281?
9.Does learning Algebra support future career opportunities for students in United Kingdom?
Explore More algebra
About BrightChamps in United Kingdom
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.
