127 LearnersLast updated on May 26th, 2025
Square Root of 3281
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 vehicle design, finance, etc. Here, we will discuss the square root of 3281.
What is the Square Root of 3281?
The square root is the inverse of the square of a number. 3281 is not a perfect square. The square root of 3281 is expressed in both radical and exponential form. In radical form, it is expressed as √3281, whereas in exponential form it is (3281)^(1/2). The value of √3281 is approximately 57.266, which is an irrational number because it cannot be expressed in the form of p/q, where p and q are integers and q ≠ 0.
Finding the Square Root of 3281
The prime factorization method is used for perfect square numbers. However, the prime factorization method is not used for non-perfect square numbers where the long division method and approximation method are used. Let us now learn the following methods:
- Prime factorization method
- Long division method
- Approximation method
Square Root of 3281 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now, let us look at how 3281 is broken down into its prime factors.
Step 1: Finding the prime factors of 3281. Breaking it down, we get 7 x 7 x 67: 7^2 x 67.
Step 2: Now that we have found the prime factors of 3281, the second step is to make pairs of those prime factors. Since 3281 is not a perfect square, the digits of the number can’t be grouped in pairs. Therefore, calculating √3281 using prime factorization is not possible.
Square Root of 3281 by Long Division Method
The long division method is particularly used for non-perfect square numbers. In this method, we should check the closest perfect square number for the given 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 3281, we need to group it as 32 and 81.
Step 2: Now we need to find n whose square is closest to 32. We can say n as ‘5’ because 5 x 5 = 25 is lesser than or equal to 32. Now the quotient is 5, and after subtracting 25 from 32, the remainder is 7.
Step 3: Now let us bring down 81, which is the new dividend. Add the old divisor with the same number 5 + 5 to get 10, which will be our new divisor.
Step 4: The new divisor will be the sum of the dividend and quotient. Now we get 10n as the new divisor; we need to find the value of n.
Step 5: The next step is finding 10n × n ≤ 781. Let us consider n as 7; now 107 x 7 = 749.
Step 6: Subtract 781 from 749; the difference is 32, and the quotient is 57.
Step 7: Since the dividend is less than the divisor, we need to add a decimal point. Adding the decimal point allows us to add two zeroes to the dividend. Now the new dividend is 3200.
Step 8: Now we need to find the new divisor that is 574 because 574 x 4 = 2296.
Step 9: Subtracting 2296 from 3200, we get the result 904.
Step 10: Now the quotient is 57.2.
Step 11: Continue doing these steps until we get two numbers after the decimal point. Suppose if there is no decimal values, continue till the remainder is zero. So the square root of √3281 is approximately 57.27.
Square Root of 3281 by Approximation Method
The approximation method is another method for finding square roots. It is an easy method to find the square root of a given number. Now let us learn how to find the square root of 3281 using the approximation method.
Step 1: Now we have to find the closest perfect square of √3281. The smallest perfect square less than 3281 is 3249, and the largest perfect square greater than 3281 is 3364. √3281 falls somewhere between 57 and 58.
Step 2: Now we need to apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Going by the formula (3281 - 3249) ÷ (3364 - 3249) = 32 ÷ 115 ≈ 0.278. Using the formula, we identified the decimal part of our square root. The next step is adding the value we got initially to the decimal number, which is 57 + 0.278 = 57.278, so the square root of 3281 is approximately 57.28.
Common Mistakes and How to Avoid Them in the Square Root of 3281
Students often 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 these 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 typically take only the positive square root, as it is often the required one.
For example: √50 = 7.07, but there is also -7.07 which should not be forgotten.
Mistake 2
Not adding the 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 before moving on to the second step.
For example: √(12+24) = √12 + √24 is incorrect. The correct way is √(12+24) = √36 = 6.
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 is incorrect; the correct answer is √50 ≈ 7.071.
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 avoid mistakes.
For example: √50 and ∛50 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. This may occur during subtraction or elsewhere in the process.
Square Root of 3281 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √3281?
The area of the square is 3281 square units.
Explanation
The area of the square = side^2.
The side length is given as √3281.
Area of the square = side^2 = √3281 x √3281 = 3281.
Therefore, the area of the square box is 3281 square units.
Problem 2
A square-shaped building measuring 3281 square feet is built; if each of the sides is √3281, what will be the square feet of half of the building?
1640.5 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 3281 by 2, we get 1640.5.
So, half of the building measures 1640.5 square feet.
Problem 3
Calculate √3281 x 5.
Approximately 286.33
Explanation
The first step is to find the square root of 3281, which is approximately 57.27. The second step is to multiply 57.27 by 5. So, 57.27 x 5 ≈ 286.33.
Problem 4
What will be the square root of (3281 + 19)?
The square root is approximately 57.74
Explanation
To find the square root, we need to find the sum of (3281 + 19). 3281 + 19 = 3300, and then √3300 is approximately 57.74. Therefore, the square root of (3281 + 19) is approximately ±57.74.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √3281 units and the width ‘w’ is 38 units.
The perimeter of the rectangle is approximately 190.54 units.
Explanation
Perimeter of the rectangle = 2 × (length + width). Perimeter = 2 × (√3281 + 38) ≈ 2 × (57.27 + 38) ≈ 2 × 95.27 ≈ 190.54 units.
FAQ on Square Root of 3281
1.What is √3281 in its simplest form?
2.Mention the factors of 3281.
3.Calculate the square of 3281.
4.Is 3281 a prime number?
5.3281 is divisible by?
6.How does learning Algebra help students in Saudi Arabia make better decisions in daily life?
7.How can cultural or local activities in Saudi Arabia support learning Algebra topics such as Square Root of 3281?
8.How do technology and digital tools in Saudi Arabia support learning Algebra and Square Root of 3281?
9.Does learning Algebra support future career opportunities for students in Saudi Arabia?
Important Glossaries for the Square Root of 3281
- Square root: A square root is the inverse of a square. Example: 5^2 = 25, and the inverse of the square is the square root, that is √25 = 5.
- Irrational number: An irrational number is a number that cannot be written 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 due to its applications in the real world. This is known as the principal square root.
- Prime factorization: Breaking down a number into its prime number components, which can be multiplied to obtain the original number.
- Long division method: A method used to find the square root of a non-perfect square number by dividing the number into smaller, more manageable parts.
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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
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