120 LearnersLast updated on May 26th, 2025
Square Root of 3267
If a number is multiplied by itself, the result is a square. The inverse operation is finding the square root. The square root is used in various fields like vehicle design, finance, etc. Here, we will discuss the square root of 3267.
What is the Square Root of 3267?
The square root is the inverse operation of squaring a number. 3267 is not a perfect square. The square root of 3267 is expressed in both radical and exponential forms. In the radical form, it is expressed as √3267, whereas in exponential form, it is expressed as (3267)^(1/2). √3267 ≈ 57.144, 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 3267
The prime factorization method is generally used for perfect square numbers. For non-perfect square numbers like 3267, 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 3267 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 3267 is broken down into its prime factors.
Step 1: Finding the prime factors of 3267 Breaking it down, we get 3 x 3 x 3 x 11 x 11: 3^3 x 11^2
Step 2: Now we have found the prime factors of 3267. The second step is to make pairs of those prime factors. Since 3267 is not a perfect square, the digits of the number can't be grouped into pairs. Therefore, calculating 3267 using prime factorization does not yield an integer result.
Square Root of 3267 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 3267, we need to group it as 67 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, which is less than 32. Now the quotient is 5, and after subtracting 5^2 from 32, the remainder is 7.
Step 3: Bring down 67 to make the new dividend 767. Add the old divisor multiplied by 2, 5 x 2 = 10, which will be our new divisor.
Step 4: The new divisor will be 10n, and we need to find the value of n.
Step 5: The next step is finding 10n × n ≤ 767. Let us consider n as 7, now 107 x 7 = 749. Step 6: Subtract 749 from 767, and the remainder is 18. The quotient now is 57.
Step 7: Since the dividend is less than the divisor, we need to add a decimal point. This allows us to add two zeroes to the dividend, making it 1800.
Step 8: The new divisor becomes 114 because 114 x 1 = 114.
Step 9: Subtracting 114 from 1800 gives 1686.
Step 10: Now the quotient is 57.1
Step 11: Continue these steps until you get two numbers after the decimal point. If there are no decimal values, continue until the remainder is zero. So the square root of √3267 ≈ 57.14.
Square Root of 3267 by Approximation Method
The approximation method is another way to find square roots, and 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 3267 using the approximation method.
Step 1: Now we have to find the closest perfect squares around √3267. The closest perfect squares are 3249 (57^2) and 3364 (58^2). √3267 falls 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, (3267 - 3249) ÷ (3364 - 3249) = 18 ÷ 115 ≈ 0.157 Using the formula, we identified the decimal point of our square root. The next step is adding the value we got initially to the decimal number, which is 57 + 0.157 = 57.157, so the square root of 3267 is approximately 57.157.
Common Mistakes and How to Avoid Them in the Square Root of 3267
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 in detail.
Mistake 1
Forgetting about the negative square root
It is important to remind students that a number has both positive and negative square roots. However, we usually consider 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 symbol properly is another common mistake. It's important to simplify the numbers inside the square root before proceeding.
For example: √(12 + 24) ≠ √12 + √24. The correct way is √(12 + 24) = √36 = 6.
Mistake 3
Not finding the correct value of a non-perfect square
The first step in finding a square root is to simplify the numbers inside the root, which is crucial to avoid mistakes in approximating the value.
For example: √50 ≈ 7.07, not 7.
Mistake 4
Confusing the square root symbol with the cube root
Students need to be taught the difference between a cube root and a square root to avoid confusion.
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. Students might accidentally skip a step, leading to incorrect results. This may occur in subtraction or other steps.
Square root of 3267 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √3267?
The area of the square is approximately 3267 square units.
Explanation
The area of a square = side^2.
The side length is given as √3267.
Area of the square = side^2 = √3267 x √3267 = 3267.
Therefore, the area of the square box is approximately 3267 square units.
Problem 2
A square-shaped building measuring 3267 square feet is built; if each of the sides is √3267, what will be the square feet of half of the building?
Approximately 1633.5 square feet.
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 3267 by 2 = 1633.5.
So half of the building measures approximately 1633.5 square feet.
Problem 3
Calculate √3267 x 5.
Approximately 285.72
Explanation
The first step is to find the square root of 3267, which is approximately 57.144.
The second step is to multiply 57.144 by 5.
So 57.144 x 5 ≈ 285.72.
Problem 4
What will be the square root of (3267 + 33)?
The square root is 58.
Explanation
To find the square root, we first find the sum of (3267 + 33).
3267 + 33 = 3300, and then √3300 ≈ 57.449.
Therefore, the square root of (3267 + 33) is approximately ±57.449.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √3267 units and the width ‘w’ is 38 units.
The perimeter of the rectangle is approximately 190.288 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√3267 + 38) = 2 × (57.144 + 38) ≈ 2 × 95.144 = 190.288 units.
FAQ on Square Root of 3267
1.What is √3267 in its simplest form?
2.Mention the factors of 3267.
3.Calculate the square of 3267.
4.Is 3267 a prime number?
5.3267 is divisible by?
6.How does learning Algebra help students in Philippines make better decisions in daily life?
7.How can cultural or local activities in Philippines support learning Algebra topics such as Square Root of 3267?
8.How do technology and digital tools in Philippines support learning Algebra and Square Root of 3267?
9.Does learning Algebra support future career opportunities for students in Philippines?
Important Glossaries for the Square Root of 3267
- Square root: A square root is the inverse operation of squaring a number. Example: 4^2 = 16, and the square root is √16 = 4.
- Irrational number: An irrational number 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. The positive square root is more commonly used and is known as the principal square root.
- Decimal: A decimal number consists of a whole number and a fractional part represented together, for example, 7.86, 8.65, and 9.42.
- Prime factorization: The expression of a number as the product of its prime factors, for example, the prime factorization of 3267 is 3^3 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.
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