101 LearnersLast updated on May 26th, 2025
Square Root of 4420
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 4420.
What is the Square Root of 4420?
The square root is the inverse of the square of the number. 4420 is not a perfect square. The square root of 4420 is expressed in both radical and exponential form. In the radical form, it is expressed as √4420, whereas (4420)^(1/2) in the exponential form. √4420 ≈ 66.4529, 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 4420
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 4420 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 4420 is broken down into its prime factors:
Step 1: Finding the prime factors of 4420
Breaking it down, we get 2 x 2 x 5 x 13 x 17
Step 2: Now we found out the prime factors of 4420. The second step is to make pairs of those prime factors. Since 4420 is not a perfect square, therefore the digits of the number can’t be grouped in pairs. Therefore, calculating 4420 using prime factorization is impossible.
Square Root of 4420 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 4420, we need to group it as 20 and 44.
Step 2: Now we need to find n whose square is closest to 44. We can say n is ‘6’ because 6 x 6 = 36 is lesser than or equal to 44. Now the quotient is 6; after subtracting 36 from 44, the remainder is 8.
Step 3: Now let us bring down 20, which is the new dividend. Add the old divisor with the same number 6 + 6, we get 12, which will be our new divisor.
Step 4: The new divisor will be the sum of the dividend and quotient. Now we get 12n as the new divisor, we need to find the value of n.
Step 5: The next step is finding 12n x n ≤ 820. Let us consider n as 6; now 126 x 6 = 756. Step 6: Subtract 756 from 820, the difference is 64, and the quotient is 66.
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 6400.
Step 8: Now we need to find the new divisor that is 132 because 1324 x 4 = 5296.
Step 9: Subtracting 5296 from 6400, we get the result 1104.
Step 10: Now the quotient is 66.4. 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 √4420 ≈ 66.45.
Square Root of 4420 by Approximation Method
The approximation method is another method for finding the 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 4420 using the approximation method.
Step 1: Now we have to find the closest perfect square of √4420. The smallest perfect square of 4420 is 4356, and the largest perfect square of 4420 is 4489. √4420 falls somewhere between 66 and 67.
Step 2: Now we need to apply the formula that is (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Going by the formula (4420 - 4356) ÷ (4489 - 4356) = 0.4529. 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 which is 66 + 0.4529 = 66.4529, so the square root of 4420 is approximately 66.4529.
Common Mistakes and How to Avoid Them in the Square Root of 4420
Students do make mistakes while finding the square root, like 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: √50 = 7.07; there is also -7.07, which should not be forgotten.
Square root of 4420 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √4420?
The area of the square is approximately 4420 square units.
Explanation
The area of the square = side².
The side length is given as √4420.
Area of the square = side² = √4420 x √4420 = 4420 square units.
Therefore, the area of the square box is 4420 square units.
Problem 2
A square-shaped building measuring 4420 square feet is built; if each of the sides is √4420, what will be the square feet of half of the building?
2210 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 4420 by 2, we get 2210.
So half of the building measures 2210 square feet.
Problem 3
Calculate √4420 x 5.
Approximately 332.2645
Explanation
The first step is to find the square root of 4420, which is approximately 66.4529; the second step is to multiply 66.4529 with 5.
So 66.4529 x 5 ≈ 332.2645.
Problem 4
What will be the square root of (4420 + 69)?
Approximately 67.
Explanation
To find the square root, we need to find the sum of (4420 + 69). 4420 + 69 = 4489, and then √4489 = 67.
Therefore, the square root of (4420 + 69) is ±67.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √4420 units and the width ‘w’ is 100 units.
We find the perimeter of the rectangle as approximately 332.9058 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√4420 + 100) ≈ 2 × (66.4529 + 100) ≈ 2 × 166.4529 ≈ 332.9058 units.
FAQ on Square Root of 4420
1.What is √4420 in its simplest form?
2.Mention the factors of 4420.
3.Calculate the square of 4420.
4.Is 4420 a prime number?
5.4420 is divisible by?
6.How does learning Algebra help students in Singapore make better decisions in daily life?
7.How can cultural or local activities in Singapore support learning Algebra topics such as Square Root of 4420?
8.How do technology and digital tools in Singapore support learning Algebra and Square Root of 4420?
9.Does learning Algebra support future career opportunities for students in Singapore?
Important Glossaries for the Square Root of 4420
- 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; however, it is always a positive square root that has more prominence due to its uses in the real world. That is the reason it is also known as a principal square root.
- Prime factorization: The process of expressing a number as a product of its prime factors.
- Long division method: A step-by-step method to find the square root of non-perfect squares by 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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