123 LearnersLast updated on May 26th, 2025
Square Root of 267
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 267.
What is the Square Root of 267?
The square root is the inverse of the square of a number. 267 is not a perfect square. The square root of 267 is expressed in both radical and exponential form. In radical form, it is expressed as √267, whereas (267)^(1/2) in exponential form. √267 ≈ 16.3401, 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 267
The prime factorization method is used for perfect square numbers. However, for non-perfect square numbers, the prime factorization method is not used; instead, 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 267 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let's look at how 267 is broken down into its prime factors:
Step 1: Finding the prime factors of 267
Breaking it down, we get 3 × 89: 3^1 × 89^1
Step 2: We have found the prime factors of 267. The second step is to make pairs of those prime factors. Since 267 is not a perfect square, the digits of the number can’t be grouped in pairs. Therefore, calculating 267 using the prime factorization method is not feasible for finding an exact square root.
Square Root of 267 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 267, we need to group it as 67 and 2.
Step 2: Now we need to find n whose square is ≤ 2. We can say n is ‘1’ because 1 × 1 is less than or equal to 2. The quotient is 1, and after subtracting 1 × 1 from 2, the remainder is 1.
Step 3: Bring down 67, making the new dividend 167. Add the old divisor with the same number: 1 + 1 = 2, which will be our new divisor.
Step 4: The new divisor will be the sum of the dividend and quotient. Now we get 2n as the new divisor, and we need to find the value of n.
Step 5: The next step is finding 2n × n ≤ 167. Let us consider n as 6; now 26 × 6 = 156.
Step 6: Subtract 156 from 167; the difference is 11, and the quotient is 16.
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 zeros to the dividend. Now the new dividend is 1100.
Step 8: Now we need to find the new divisor. Let's try n as 3 because 326 × 3 = 978.
Step 9: Subtract 978 from 1100; we get the result 122.
Step 10: Now the quotient is 16.3.
Step 11: Continue doing these steps until you get two numbers after the decimal point. If there are no decimal values, continue till the remainder is zero.
So the square root of √267 is approximately 16.34.
Square Root of 267 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 267 using the approximation method.
Step 1: Now we have to find the closest perfect squares around √267. The smallest perfect square less than 267 is 256, and the largest perfect square greater than 267 is 289. √267 falls somewhere between 16 and 17.
Step 2: Now we need to apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square) Using the formula: (267 - 256) / (289 - 256) ≈ 0.34 Combining this with the smaller integer, we get approximately 16 + 0.34 = 16.34.
So the square root of 267 is approximately 16.34.
Common Mistakes and How to Avoid Them in the Square Root of 267
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. Let's explore a few common mistakes in detail.
Mistake 1
Forgetting about the negative square root
It is important to remember that a number has both positive and negative square roots. However, we typically take the positive square root, as it is the required one in most practical scenarios.
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
Incorrect use of the square root symbol is another mistake that students make. To resolve this, students need to be taught to simplify the numbers inside the square root first, then proceed to further calculations.
For example, √(12+24) ≠ √12 + √24. The correct method is √(12+24) = √36.
Mistake 3
Not finding the correct value of a non-perfect square
It's important to simplify numbers inside the square root correctly to avoid mistakes in identifying the approximate value.
For example, saying √50 = 7 is incorrect; the correct answer is √50 ≈ 7.071067.
Mistake 4
Confusing the square root symbol with the cube root
Students need to clearly distinguish between cube roots and square roots to avoid confusion.
For example, √50 and ∛50 are different operations.
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, resulting in a wrong answer. This may happen in subtraction or elsewhere.
Square Root of 267 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √267?
The area of the square is approximately 712.89 square units.
Explanation
The area of the square = side².
The side length is given as √267.
Area of the square = (√267)² = 267.
Therefore, the area of the square box is approximately 712.89 square units.
Problem 2
A square-shaped building measuring 267 square feet is built. If each of the sides is √267, what will be the square feet of half of the building?
133.5 square feet
Explanation
We can divide the given area by 2 since the building is square-shaped.
Dividing 267 by 2 gives us 133.5.
So half of the building measures 133.5 square feet.
Problem 3
Calculate √267 × 5.
Approximately 81.7
Explanation
The first step is to find the square root of 267, which is approximately 16.34.
The second step is to multiply 16.34 by 5.
So, 16.34 × 5 ≈ 81.7.
Problem 4
What will be the square root of (267 + 1)?
The square root is 16.
Explanation
To find the square root, we need to find the sum of (267 + 1). 267 + 1 = 268, and then √268 ≈ 16.3707.
Therefore, the square root of 268 is approximately ±16.37.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √267 units and the width ‘w’ is 38 units.
The perimeter of the rectangle is approximately 108.68 units.
Explanation
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√267 + 38) = 2 × (16.34 + 38) = 2 × 54.34 ≈ 108.68 units.
FAQ on Square Root of 267
1.What is √267 in its simplest form?
2.Mention the factors of 267.
3.Calculate the square of 267.
4.Is 267 a prime number?
5.267 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 267?
8.How do technology and digital tools in Philippines support learning Algebra and Square Root of 267?
9.Does learning Algebra support future career opportunities for students in Philippines?
Important Glossaries for the Square Root of 267
- Square root: A square root is the inverse of squaring a number. Example: 4^2=16, and the inverse of the square is the square root, which is √16 = 4.
- Irrational number: An irrational number cannot be written in the form of p/q, where q is not 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 more commonly used in practical scenarios, known as the principal square root.
- Prime factorization: Breaking down a number into its prime factors. For example, the prime factorization of 267 is 3 × 89.
- Decimal: If a number has a whole number and a fractional part, it is called a decimal. For example, 16.34 is a decimal.
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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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