102 LearnersLast updated on May 26th, 2025
Square Root of 481
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 481.
What is the Square Root of 481?
The square root is the inverse of the square of the number. 481 is not a perfect square. The square root of 481 is expressed in both radical and exponential form.
In the radical form, it is expressed as √481, whereas (481)(1/2) in the exponential form. √481 ≈ 21.9317, 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 481
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 481 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 481 is broken down into its prime factors.
Step 1: Finding the prime factors of 481
Breaking it down, we get 13 × 37: 131 × 371
Step 2: Now we found out the prime factors of 481. The second step is to make pairs of those prime factors. Since 481 is not a perfect square, the digits of the number can’t be grouped in pairs.
Therefore, calculating 481 using prime factorization is impossible.
Square Root of 481 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 481, we need to group it as 81 and 4.
Step 2: Now we need to find a number 'n' whose square is less than or equal to 4. We can say n is ‘2’ because 2 × 2 = 4. Now the quotient is 2, and after subtracting 4 - 4, the remainder is 0.
Step 3: Now let us bring down 81, which is the new dividend. Add the old divisor with the same number: 2 + 2 = 4, which will be our new divisor.
Step 4: The new divisor will be the sum of the dividend and quotient. Now we get 4n as the new divisor, and we need to find the value of n.
Step 5: The next step is finding 4n × n ≤ 81. Let us consider n as 2. Now, 42 × 2 = 84, which is too large, so we try n = 1.
Step 6: Subtract 81 from 41 (4 × 10 + 1 = 41), the difference is 40, and the quotient is 21.
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 zeroes to the dividend. Now the new dividend is 4000.
Step 8: Now we need to find the new divisor that gives a product less than or equal to 4000. Let's try 429 × 9 = 3861.
Step 9: Subtracting 3861 from 4000 gives the result of 139.
Step 10: Now the quotient is 21.9.
Step 11: Continue doing these steps until we get two numbers after the decimal point. Suppose if there are no decimal values, continue till the remainder is zero.
So the square root of √481 is approximately 21.93.
Square Root of 481 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 481 using the approximation method.
Step 1: Now we have to find the closest perfect squares to √481.
The smallest perfect square less than 481 is 441, and the largest perfect square greater than 481 is 484. √481 falls somewhere between 21 and 22.
Step 2: Now we need to apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square) Going by the formula: (481 - 441) / (484 - 441) = 40/43 = 0.9302
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: 21 + 0.9302 = 21.9302
So the square root of 481 is approximately 21.9302.
Common Mistakes and How to Avoid Them in the Square Root of 481
Students do make mistakes while finding the square root, such as forgetting about the negative square root, skipping long division methods, etc. 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 does have both positive and negative square roots. However, we will be taking only the positive square root, as it is the required one.
For example: √25 = 5, there is also -5 which should not be forgotten.
Square Root of 481 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √481?
The area of the square is approximately 481 square units.
Explanation
The area of the square = side².
The side length is given as √481.
Area of the square = side² = √481 × √481 = 481.
Therefore, the area of the square box is approximately 481 square units.
Problem 2
A square-shaped building measuring 481 square feet is built; if each of the sides is √481, what will be the square feet of half of the building?
240.5 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 481 by 2 = we get 240.5.
So half of the building measures 240.5 square feet.
Problem 3
Calculate √481 × 5.
Approximately 109.66
Explanation
The first step is to find the square root of 481, which is approximately 21.93.
The second step is to multiply 21.93 by 5.
So 21.93 × 5 ≈ 109.66.
Problem 4
What will be the square root of (441 + 40)?
The square root is approximately 21.93.
Explanation
To find the square root, we need to find the sum of (441 + 40). 441 + 40 = 481, and then √481 ≈ 21.93.
Therefore, the square root of (441 + 40) is ±21.93.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √481 units and the width ‘w’ is 38 units.
The perimeter of the rectangle is approximately 119.86 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√481 + 38) ≈ 2 × (21.93 + 38) = 2 × 59.93 ≈ 119.86 units.
FAQ on Square Root of 481
1.What is √481 in its simplest form?
2.Mention the factors of 481.
3.Calculate the square of 481.
4.Is 481 a prime number?
5.481 is divisible by?
6.How does learning Algebra help students in United States make better decisions in daily life?
7.How can cultural or local activities in United States support learning Algebra topics such as Square Root of 481?
8.How do technology and digital tools in United States support learning Algebra and Square Root of 481?
9.Does learning Algebra support future career opportunities for students in United States?
Important Glossaries for the Square Root of 481
- Square root: A square root is the inverse of a square. Example: 4² = 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, but it is usually the positive square root that is used in practical applications.
- Prime factorization: The process of expressing a number as the product of its prime factors.
- Long division method: A step-by-step approach for finding square roots of non-perfect squares by grouping numbers and dividing them systematically.
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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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