131 LearnersLast updated on May 26th, 2025
Square Root of 3280
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 3280.
What is the Square Root of 3280?
The square root is the inverse of the square of the number. 3280 is not a perfect square. The square root of 3280 is expressed in both radical and exponential form. In radical form, it is expressed as √3280, whereas in exponential form it is expressed as (3280)^(1/2). √3280 ≈ 57.276, 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 3280
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 3280 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 3280 is broken down into its prime factors.
Step 1: Finding the prime factors of 3280 Breaking it down, we get 2 x 2 x 2 x 2 x 5 x 41: 2^4 x 5 x 41
Step 2: Now we have found the prime factors of 3280. The second step is to make pairs of those prime factors. Since 3280 is not a perfect square, the digits of the number can’t be grouped into pairs. Therefore, calculating 3280 using prime factorization is not straightforward.
Square Root of 3280 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 3280, we group it as 80 and 32.
Step 2: Now we need to find n whose square is less than or equal to 32. We can say n is '5' because 5 x 5 = 25 is less than 32. Now the quotient is 5, and after subtracting 25 from 32, the remainder is 7.
Step 3: Now let us bring down 80 which is the new dividend. Add the old divisor with the same number 5 + 5 = 10, which will be our new divisor.
Step 4: The new divisor will be 10n. We need to find the largest n such that 10n x n ≤ 780. Let's consider n as 7, now 107 x 7 = 749.
Step 5: Subtracting 749 from 780, the difference is 31, and the quotient is 57.
Step 6: 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 3100.
Step 7: Now we need to find the new divisor that is 574 because 574 x 4 = 2296.
Step 8: Subtracting 2296 from 3100, we get the result 804.
Step 9: Continue doing these steps until we get two numbers after the decimal point. So the square root of √3280 is approximately 57.28.
Square Root of 3280 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 3280 using the approximation method.
Step 1: Now we have to find the closest perfect square of √3280. The smallest perfect square less than 3280 is 3249 (57^2) and the largest perfect square less than 3280 is 3364 (58^2). √3280 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). Using the approximation formula (3280 - 3249) / (3364 - 3249) = 31 / 115 ≈ 0.2696 Adding this to the smaller root, we get 57 + 0.2696 = 57.2696. Therefore, the approximate square root of 3280 is 57.27.
Common Mistakes and How to Avoid Them in the Square Root of 3280
Students often make mistakes while finding the square root, like forgetting about the negative square root or skipping long division methods. 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 typically consider only the positive square root, as it is the required one in many practical applications.
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 students make. To resolve this, we need to teach students that simplifying the numbers inside the square root is important before moving on to the second step.
For example: √(12+24) ≠ √12 + √24. The correct approach is √(12+24) = √36.
Mistake 3
Not finding the correct value of a non-perfect square
The first step that needs to be taught to students is to simplify the numbers inside the square root. This is important to avoid mistakes while identifying the approximate value.
For example: √50 ≠ 7; the correct answer is √50 ≈ 7.071067.
Mistake 4
Confusing the square root symbol with the cube root
Students need to be taught the difference between the cube root and square root consistently to 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 at the end of the calculation. This may happen during subtraction or elsewhere.
Square root of 3280 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √3280?
The area of the square is 3280 square units.
Explanation
The area of the square = side^2.
The side length is given as √3280.
Area of the square = side^2 = √3280 x √3280 = 3280.
Therefore, the area of the square box is 3280 square units.
Problem 2
A square-shaped building measuring 3280 square feet is built; if each of the sides is √3280, what will be the square feet of half of the building?
1640 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 3280 by 2, we get 1640.
So half of the building measures 1640 square feet.
Problem 3
Calculate √3280 x 5.
Approximately 286.38
Explanation
The first step is to find the square root of 3280, which is approximately 57.28.
The second step is to multiply 57.28 by 5.
So 57.28 x 5 ≈ 286.38.
Problem 4
What will be the square root of (3280 + 20)?
The square root is approximately 57.618.
Explanation
To find the square root, we need to find the sum of (3280 + 20).
3280 + 20 = 3300, and then √3300 ≈ 57.618.
Therefore, the square root of (3280 + 20) is ±57.618.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √3280 units and the width ‘w’ is 38 units.
We find the perimeter of the rectangle as 190.56 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√3280 + 38) = 2 × (57.28 + 38) = 2 × 95.28 = 190.56 units.
FAQ on Square Root of 3280
1.What is √3280 in its simplest form?
2.Mention the factors of 3280.
3.Calculate the square of 3280.
4.Is 3280 a prime number?
5.3280 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 3280?
8.How do technology and digital tools in Saudi Arabia support learning Algebra and Square Root of 3280?
9.Does learning Algebra support future career opportunities for students in Saudi Arabia?
Important Glossaries for the Square Root of 3280
- Square root: A square root is the inverse of a square. Example: 4^2 = 16, and the inverse of the square is the square root, that is √16 = 4.
- 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; however, it is always the positive square root that has more prominence due to its uses in the real world. That is why it is known as the principal square root.
- Prime factorization: This is the process of expressing a number as a product of its prime factors.
- Approximation method: A practical method to estimate the square root of a non-perfect square by comparing it to the nearest perfect squares.
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About BrightChamps in Saudi Arabia
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.
