130 LearnersLast updated on May 26th, 2025
Square Root of 4425
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 4425.
What is the Square Root of 4425?
The square root is the inverse of the square of the number. 4425 is not a perfect square. The square root of 4425 is expressed in both radical and exponential form. In the radical form, it is expressed as √4425, whereas (4425)^(1/2) in the exponential form. √4425 ≈ 66.4906, 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 4425
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 4425 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 4425 is broken down into its prime factors:
Step 1: Finding the prime factors of 4425
Breaking it down, we get 3 x 3 x 5 x 5 x 59.
Step 2: Now we found out the prime factors of 4425. The second step is to make pairs of those prime factors. Since 4425 is not a perfect square, therefore the digits of the number can’t be grouped in pairs entirely. Therefore, calculating 4425 using prime factorization is not straightforward.
Square Root of 4425 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 4425, we need to group it as 42 and 25.
Step 2: Now we need to find n whose square is closest to 42. We can say n as '6' because 6 x 6 = 36, which is lesser than 42. Now the quotient is 6 after subtracting 42 - 36, the remainder is 6.
Step 3: Now let us bring down 25, 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: We find n such that 12n x n ≤ 625. Let us consider n as 5, now 12 x 5 x 5 = 625.
Step 5: Subtract 625 from 625, the difference is 0, and the quotient is 65.
Step 6: Since the remainder is zero, the square root of 4425 is approximately 66.49, but the process of attaining further decimal places can continue.
Square Root of 4425 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 4425 using the approximation method.
Step 1: Now we have to find the closest perfect square of √4425. The smallest perfect square less than 4425 is 4356 (66^2) and the largest perfect square greater than 4425 is 4489 (67^2). √4425 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 (4425 - 4356) / (4489 - 4356) = 69/133 ≈ 0.518 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 + 0.518 ≈ 66.518, so the square root of 4425 is approximately 66.52.
Common Mistakes and How to Avoid Them in the Square Root of 4425
Students do make mistakes while finding the square root, likewise 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.
Mistake 2
Not adding 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 and then move on to the second step.
For Example: √(12+24) = √12 + √24 is the 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 = 7.071067.
Mistake 4
Confusing the square root symbol with the cube root
Students need to be taught the difference between the cube root and square root constantly as this will help them keep away from 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 either happen in subtracting or elsewhere.
Square root of 4425 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √4425?
The area of the square is approximately 4425 square units.
Explanation
The area of the square = side².
The side length is given as √4425.
Area of the square = side² = (√4425) x (√4425) = 4425.
Therefore, the area of the square box is approximately 4425 square units.
Problem 2
A square-shaped building measuring 4425 square feet is built; if each of the sides is √4425, what will be the square feet of half of the building?
2212.5 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 4425 by 2 = we get 2212.5.
So half of the building measures 2212.5 square feet.
Problem 3
Calculate √4425 x 3.
199.4718
Explanation
The first step is to find the square root of 4425 which is approximately 66.49, the second step is to multiply 66.49 with 3.
So 66.49 x 3 ≈ 199.4718.
Problem 4
What will be the square root of (4250 + 175)?
The square root is approximately 67.
Explanation
To find the square root, we need to find the sum of (4250 + 175). 4250 + 175 = 4425, and then √4425 ≈ 66.49.
Therefore, the square root of (4250 + 175) is approximately ±67.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √4425 units and the width ‘w’ is 50 units.
We find the perimeter of the rectangle as approximately 232.98 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√4425 + 50) = 2 × (66.49 + 50) = 2 × 116.49 = 232.98 units.
FAQ on Square Root of 4425
1.What is √4425 in its simplest form?
2.Mention the factors of 4425.
3.Calculate the square of 4425.
4.Is 4425 a prime number?
5.4425 is divisible by?
6.How does learning Algebra help students in Bahrain make better decisions in daily life?
7.How can cultural or local activities in Bahrain support learning Algebra topics such as Square Root of 4425?
8.How do technology and digital tools in Bahrain support learning Algebra and Square Root of 4425?
9.Does learning Algebra support future career opportunities for students in Bahrain?
Important Glossaries for the Square Root of 4425
- Square root: A square root is a value that, when multiplied by itself, gives the original number. Example: 4^2 = 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: Prime factorization is the process of expressing a number as a product of its prime factors. Example: The prime factorization of 28 is 2 x 2 x 7.
- Decimal: If a number has a whole number and a fraction in a single number, then it is called a decimal. For example: 7.86, 8.65, and 9.42 are decimals.
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About BrightChamps in Bahrain
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
: He loves to play the quiz with kids through algebra to make kids love it.
