123 LearnersLast updated on May 26th, 2025
Square Root of 281
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 like vehicle design, finance, etc. Here, we will discuss the square root of 281.
What is the Square Root of 281?
The square root is the inverse of the square of a number. 281 is not a perfect square. The square root of 281 is expressed in both radical and exponential form. In the radical form, it is expressed as √281, whereas (281)^(1/2) in exponential form. √281 ≈ 16.763, 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 281
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 281 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 281 is broken down into its prime factors:
Step 1: Finding the prime factors of 281 281 is a prime number, so it cannot be broken down into other prime factors. Therefore, calculating 281 using prime factorization is not applicable.
Square Root of 281 by Long Division Method
The long division method is particularly used for non-perfect square numbers. Let us learn how to find the square root using the long division method, step by step:
Step 1: To begin with, group the digits of 281 from right to left. In this case, 281 is already a single group.
Step 2: Find a number n whose square is less than or equal to 2. Here, n is 1 because 1^2 = 1 and is less than 2.
Step 3: Subtract 1 from 2, and the remainder is 1. Bring down the next pair (81) to get 181.
Step 4: Double the divisor (1) to get 2. Now find the largest digit x such that 2x * x ≤ 181, which is x = 6.
Step 5: Calculate 26 * 6 = 156. Subtract 156 from 181 to get 25.
Step 6: Bring down two zeros to make it 2500.
Step 7: Double the quotient 16 to get 32. Find x such that 32x * x ≤ 2500. This gives x = 7.
Step 8: Calculate 327 * 7 = 2289. Subtract 2289 from 2500 to get 211.
Step 9: Continue this process until the desired number of decimal places is reached. The square root of 281 is approximately 16.763.
Square Root of 281 by Approximation Method
The approximation method is an easy way to find the square root of a given number. Now let us learn how to find the square root of 281 using the approximation method.
Step 1: Find the closest perfect squares around 281. The nearest perfect squares are 256 (16^2) and 289 (17^2). Therefore, √281 is between 16 and 17.
Step 2: Apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square) Using the formula, (281 - 256) / (289 - 256) = 25 / 33 ≈ 0.757 Adding this to the smaller perfect square root: 16 + 0.757 = 16.757 Thus, the approximate square root of 281 is 16.757.
Common Mistakes and How to Avoid Them in the Square Root of 281
Students often make mistakes while finding the square root, such as forgetting about the negative square root, skipping steps in the long division method, etc. Let us look at some 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 usually take only the positive square root for practical purposes.
For example, √50 ≈ 7.071, but there is also -7.071.
Mistake 2
Not adding square root symbol in proper places
Not using the square root symbol properly is a common mistake. Students should simplify the expression inside the square root before proceeding.
For example, √(12 + 24) = √36, not √12 + √24.
Mistake 3
Not finding the correct value of a non-perfect square
Students should accurately approximate the value of non-perfect square roots.
For example, √50 ≈ 7.071, not 7.
Mistake 4
Confusing the square root symbol with the cube root
Students need to distinguish between the square root and cube root symbols.
For example, √50 and ∛50 are different calculations.
Mistake 5
Making mistakes in long division
Finding a square root using the long division method involves many steps. Students can easily skip a step, leading to incorrect results. Careful attention to each step is crucial.
Square Root of 281 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √281?
The area of the square is approximately 789.69 square units.
Explanation
The area of the square = side^2.
The side length is given as √281.
Area of the square = side^2 = (√281) × (√281) = 281.
Therefore, the area of the square box is approximately 789.69 square units.
Problem 2
A square-shaped building measuring 281 square feet is built; if each of the sides is √281, what will be the square feet of half of the building?
140.5 square feet
Explanation
We can divide the given area by 2 as the building is square-shaped.
Dividing 281 by 2 = 140.5
So half of the building measures 140.5 square feet.
Problem 3
Calculate √281 × 5.
Approximately 83.815
Explanation
The first step is to find the square root of 281, which is approximately 16.763.
The second step is to multiply 16.763 by 5.
Therefore, 16.763 × 5 ≈ 83.815.
Problem 4
What will be the square root of (275 + 6)?
The square root is 17.
Explanation
To find the square root, calculate the sum of (275 + 6) = 281, and then √281 ≈ 16.763.
Therefore, the square root of (275 + 6) is approximately ±16.763.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √281 units and the width ‘w’ is 38 units.
The perimeter of the rectangle is approximately 109.53 units.
Explanation
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√281 + 38) = 2 × (16.763 + 38) = 2 × 54.763 = 109.526 units.
FAQ on Square Root of 281
1.What is √281 in its simplest form?
2.Mention the factors of 281.
3.Calculate the square of 281.
4.Is 281 a prime number?
5.281 is divisible by?
6.How does learning Algebra help students in Thailand make better decisions in daily life?
7.How can cultural or local activities in Thailand support learning Algebra topics such as Square Root of 281?
8.How do technology and digital tools in Thailand support learning Algebra and Square Root of 281?
9.Does learning Algebra support future career opportunities for students in Thailand?
Important Glossaries for the Square Root of 281
- Square root: A square root is a value that, when multiplied by itself, gives the original number. For example, the square root of 16 is 4, as 4 × 4 = 16.
- Irrational number: An irrational number cannot be expressed as a simple fraction. Its decimal goes on forever without repeating. For example, √281 is an irrational number.
- Principal square root: The non-negative square root of a number. For example, the principal square root of 9 is 3.
- Prime number: A number greater than 1 that has no positive divisors other than 1 and itself. For example, 281 is a prime number.
- Decimal approximation: The process of finding a decimal value close to the actual value of an irrational number. For example, √281 ≈ 16.763.
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About BrightChamps in Thailand
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.
