161 LearnersLast updated on May 26th, 2025
Square Root of 4489
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 fields of vehicle design, finance, etc. Here, we will discuss the square root of 4489.
What is the Square Root of 4489?
The square root is the inverse of the square of a number. 4489 is a perfect square. The square root of 4489 can be expressed in both radical and exponential form. In radical form, it is expressed as √4489, whereas in exponential form, it is (4489)^(1/2). √4489 = 67, which is a rational number because it can be expressed in the form of p/q, where p and q are integers and q ≠ 0.
Finding the Square Root of 4489
The prime factorization method can be used for perfect square numbers. However, for non-perfect square numbers, the long-division method and approximation method are also used. Let us now learn the following methods:
- Prime factorization method
- Long division method
- Approximation method
Square Root of 4489 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 4489 is broken down into its prime factors.
Step 1: Finding the prime factors of 4489
Breaking it down, we get 67 × 67: 67^2
Step 2: Now we found out the prime factors of 4489. The next step is to make pairs of those prime factors. Since 4489 is a perfect square, we can pair the digits. Therefore, calculating 4489 using prime factorization gives us √4489 = 67.
Square Root of 4489 by Long Division Method
The long division method is particularly used for non-perfect square numbers, but it can also verify perfect squares. In this method, we will 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 4489, we need to group it as 44 and 89.
Step 2: Now we need to find n whose square is less than or equal to 44. We can say n is ‘6’ because 6 × 6 = 36, which is less than 44. Now the quotient is 6, and the remainder after subtracting 36 from 44 is 8.
Step 3: Now let us bring down 89 to make the new dividend 889. Add the old divisor with the same number 6 + 6 to get 12, which will be our new divisor.
Step 4: The new divisor will be 12n. We need to find the value of n such that 12n × n is less than or equal to 889. Let us consider n as 7, now 12 × 7 × 7 = 889.
Step 5: Subtract 889 from 889, the difference is 0, and the quotient is 67. Therefore, the square root of √4489 is 67.
Square Root of 4489 by Approximation Method
The approximation method is another method for finding square roots, used especially for non-perfect squares, but it is straightforward for perfect squares. Since 4489 is a perfect square, the approximation method provides quick verification.
Step 1: Identify the closest perfect square of √4489. Since 4489 is already a perfect square, we know √4489 = 67.
Step 2: Therefore, the square root of 4489 is 67.
Common Mistakes and How to Avoid Them in the Square Root of 4489
Students do make mistakes while finding the square root, such as forgetting about the negative square root or skipping long division methods. Now let us look at a few of those mistakes in detail.
Mistake 1
Forgetting about the negative square root
It is important to make students aware that a number has both positive and negative square roots. However, we generally take only the positive square root, as it is the required one in most contexts.
For example: √4489 = 67, there is also -67, which should not be forgotten.
Mistake 2
Not adding the square root symbol in proper places
Not using the square root properly is another mistake that children make. To resolve this, we need to teach children that simplifying the numbers inside the square root is important before moving on to the next step.
For Example: √(12+24) = √12 + √24 is a wrong method of using roots.
The right way of using roots is √(12+24) = √36.
Mistake 3
Not finding the correct value of a non-perfect square
The first step that needs to be taught to children is to simplify the numbers inside the square root. This is important so that students do not make mistakes while identifying the approximate value.
For Example: √50 = 7 is wrong; the correct answer is √50 ≈ 7.071.
Mistake 4
Confusing the square root symbol with the cube root
Students need to be taught the difference between cube root and square root constantly, as this will help them avoid mistakes.
For Example: √50 and ∛50 are different.
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, which results in a wrong answer at the end of the sum. This may happen either in subtracting or elsewhere.
Square Root of 4489 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √4489?
The area of the square is 4489 square units.
Explanation
The area of the square = side^2.
The side length is given as √4489.
Area of the square = (√4489)^2 = 67 × 67 = 4489.
Therefore, the area of the square box is 4489 square units.
Problem 2
A square-shaped garden measuring 4489 square feet is built; if each of the sides is √4489, what will be the square feet of half of the garden?
2244.5 square feet
Explanation
We can just divide the given area by 2 as the garden is square-shaped.
Dividing 4489 by 2 = 2244.5.
So half of the garden measures 2244.5 square feet.
Problem 3
Calculate √4489 × 3.
201
Explanation
The first step is to find the square root of 4489, which is 67.
The second step is to multiply 67 by 3.
So 67 × 3 = 201.
Problem 4
What will be the square root of (4489 + 121)?
The square root is 70.
Explanation
To find the square root, we need to find the sum of (4489 + 121). 4489 + 121 = 4609, and then √4609 = 70.
Therefore, the square root of (4489 + 121) is ±70.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √4489 units and the width ‘w’ is 10 units.
The perimeter of the rectangle is 154 units.
Explanation
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√4489 + 10) = 2 × (67 + 10) = 2 × 77 = 154 units.
FAQ on Square Root of 4489
1.What is √4489 in its simplest form?
2.Mention the factors of 4489.
3.Calculate the square of 67.
4.Is 4489 a prime number?
5.4489 is divisible by?
6.How does learning Algebra help students in Vietnam make better decisions in daily life?
7.How can cultural or local activities in Vietnam support learning Algebra topics such as Square Root of 4489?
8.How do technology and digital tools in Vietnam support learning Algebra and Square Root of 4489?
9.Does learning Algebra support future career opportunities for students in Vietnam?
Important Glossaries for the Square Root of 4489
- Square root: A square root is the inverse of a square. Example: 4^2 = 16, and the inverse of the square is the square root, that is, √16 = 4.
- Rational number: A rational number is a number that can be expressed in the form of p/q, where q is not equal to zero and p and q are integers.
- Perfect square: A perfect square is a number that is the square of an integer. Example: 36 is a perfect square because it is 6^2.
- Prime factorization: Prime factorization is the process of expressing a number as the product of its prime factors.
- Long division method: A method used to find the square root of a number that involves dividing and averaging.
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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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