Last updated on May 26th, 2025
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.
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.
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:
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.
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.
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.
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.
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.
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.
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
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.
Calculate √281 × 5.
Approximately 83.815
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.
What will be the square root of (275 + 6)?
The square root is 17.
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.
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.
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√281 + 38) = 2 × (16.763 + 38) = 2 × 54.763 = 109.526 units.
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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