124 LearnersLast updated on May 26th, 2025
Square Root of 4481
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 such as vehicle design, finance, etc. Here, we will discuss the square root of 4481.
What is the Square Root of 4481?
The square root is the inverse of the square of the number. 4481 is not a perfect square. The square root of 4481 is expressed in both radical and exponential form. In radical form, it is expressed as √4481, whereas in exponential form, it is (4481)^(1/2). √4481 ≈ 66.96984, 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 4481
The prime factorization method is used for perfect square numbers. However, for non-perfect square numbers, methods such as the long-division method and approximation method are used. Let us now learn these methods:
- Prime factorization method
- Long division method
- Approximation method
Square Root of 4481 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 4481 is broken down into its prime factors.
Step 1: Finding the prime factors of 4481 Breaking it down, we find that 4481 cannot be easily expressed as a product of repeated prime factors, making it unsuitable for the prime factorization method to find the square root accurately. Since 4481 is not a perfect square, calculating it using prime factorization is impractical for finding the square root.
Square Root of 4481 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 digits of 4481 from right to left, which is already a single group.
Step 2: Find a number whose square is less than or equal to 44. The number is 6, as 6 × 6 = 36.
Step 3: Subtract 36 from 44, bringing down the next group to get 881.
Step 4: Double the current quotient (6), and use it as the first part of the new divisor, i.e., 12_.
Step 5: Find a digit n such that (12n) × n ≤ 881. Here n is 7, as 127 × 7 = 889, which is greater than 881. So try n = 6, then 126 × 6 = 756.
Step 6: Subtract 756 from 881 to get a remainder of 125. The current quotient is 66.
Step 7: Since the remainder is not zero, add a decimal point to the quotient and bring down two zeros to make it 12500.
Step 8: Find a new divisor, 132_, and repeat the process with the new remainder.
Step 9: Continue until you have the desired precision. The quotient becomes approximately 66.96984.
So, the square root of √4481 ≈ 66.96984.
Square Root of 4481 by Approximation Method
The approximation method is another method for finding 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 4481 using the approximation method.
Step 1: Find the closest perfect squares around 4481. The smallest perfect square less than 4481 is 4356 (66²), and the largest perfect square greater than 4481 is 4624 (68²). √4481 falls between 66 and 68.
Step 2: Apply the formula for approximation: (Given number - smaller perfect square) / (difference between perfect squares). (4481 - 4356) / (4624 - 4356) = 125 / 268 ≈ 0.4664
Step 3: Add this decimal to the smaller perfect square root: 66 + 0.4664 ≈ 66.4664 The square root of 4481 is approximately 66.97.
Common Mistakes and How to Avoid Them in the Square Root of 4481
Students often make mistakes while finding the square root, such as forgetting about the negative square root or skipping the long division steps. Let us look at a few common mistakes in detail.
Mistake 1
Forgetting about the negative square root
It is important for students to be aware that a number has both positive and negative square roots. However, we typically take only the positive square root, as it is the one required in most contexts.
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 usage of the square root symbol is a common mistake. To resolve this, students need to simplify expressions under the square root first.
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
Students should be taught to simplify expressions inside the square root to avoid errors in approximating values.
For example: √50 ≈ 7.071067, not 7.
Mistake 4
Confusing the square root symbol with the cube root
Students should be consistently reminded of the difference between square root and cube root symbols to avoid confusion.
For example: √50 and ∛50 are different.
Mistake 5
Making mistakes in long division
The long division method involves multiple steps, and students might skip steps accidentally, leading to incorrect answers. This may occur during subtraction or other steps.
Square Root of 4481 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √4481?
The area of the square is approximately 4481 square units.
Explanation
The area of the square = side².
The side length is given as √4481.
Area of the square = (√4481)² = 4481.
Therefore, the area of the square box is 4481 square units.
Problem 2
A square-shaped building measuring 4481 square feet is built; if each of the sides is √4481, what will be the square feet of half of the building?
2240.5 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 4481 by 2 = 2240.5
So half of the building measures 2240.5 square feet.
Problem 3
Calculate √4481 × 5.
Approximately 334.85
Explanation
The first step is to find the square root of 4481, which is approximately 66.97.
The second step is to multiply 66.97 by 5.
So 66.97 × 5 ≈ 334.85.
Problem 4
What will be the square root of (4481 + 19)?
The square root is approximately 67.
Explanation
To find the square root, we need to find the sum of (4481 + 19). 4481 + 19 = 4500, and then √4500 ≈ 67.08.
Therefore, the square root of (4481 + 19) is approximately 67.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √4481 units and the width ‘w’ is 38 units.
The perimeter of the rectangle is approximately 209.94 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√4481 + 38) ≈ 2 × (66.97 + 38) ≈ 2 × 104.97 ≈ 209.94 units.
FAQ on Square Root of 4481
1.What is √4481 in its simplest form?
2.Mention the factors of 4481.
3.Calculate the square of 4481.
4.Is 4481 a prime number?
5.4481 is divisible by?
6.How does learning Algebra help students in Australia make better decisions in daily life?
7.How can cultural or local activities in Australia support learning Algebra topics such as Square Root of 4481?
8.How do technology and digital tools in Australia support learning Algebra and Square Root of 4481?
9.Does learning Algebra support future career opportunities for students in Australia?
Important Glossaries for the Square Root of 4481
- Square root: A square root is the inverse of a square. Example: 4² = 16 and the inverse of the square is the square root, which 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.
- Long division method: A method used to find the square roots of non-perfect squares involving systematic division steps.
- Approximation: A method to estimate the square root of a number by comparing it to known perfect squares.
- Prime number: A number greater than 1 that has no positive divisors other than 1 and itself.
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Jaskaran Singh Saluja
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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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