130 LearnersLast updated on May 26th, 2025
Square Root of 9225
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 9225.
What is the Square Root of 9225?
The square root is the inverse of the square of a number. 9225 is not a perfect square. The square root of 9225 is expressed in both radical and exponential form. In the radical form, it is expressed as √9225, whereas (9225)^(1/2) in the exponential form. √9225 ≈ 96.06559, 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 9225
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 9225 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 9225 is broken down into its prime factors:
Step 1: Finding the prime factors of 9225
Breaking it down, we get 3 x 3 x 5 x 5 x 41 = 3² x 5² x 41
Step 2: Now that we have found the prime factors of 9225, we make pairs of those prime factors. Since 9225 is not a perfect square, the digits of the number can’t be grouped into complete pairs. Therefore, calculating 9225 using prime factorization alone is insufficient.
Square Root of 9225 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 9225, we need to group it as 25 and 92.
Step 2: Now we need to find n whose square is less than or equal to 92. We can say n is ‘9’ because 9 x 9 = 81, which is less than 92. Now the quotient is 9, and after subtracting 81 from 92, the remainder is 11.
Step 3: Now, let us bring down 25, which becomes the new dividend. Add the old divisor with the same number 9 + 9 to get 18, which will be our new divisor.
Step 4: The new divisor will be represented as 18n. We need to find the value of n such that 18n x n ≤ 1125.
Step 5: The next step is finding 18n × n ≤ 1125. Let us consider n as 6, now 186 x 6 = 1116.
Step 6: Subtract 1116 from 1125; the difference is 9, and the quotient becomes 96.
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 900.
Step 8: Now we need to find the new divisor, which is 193, because 193 x 4 = 772.
Step 9: Subtracting 772 from 900, we get the result 128.
Step 10: Now the quotient is 96.0.
Step 11: Continue doing these steps until we get two numbers after the decimal point.
So the square root of √9225 is approximately 96.06.
Square Root of 9225 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 9225 using the approximation method.
Step 1: We have to find the closest perfect squares to √9225. The smallest perfect square less than 9225 is 9216 (96²), and the largest perfect square greater than 9225 is 9409 (97²). Thus, √9225 falls between 96 and 97.
Step 2: Now we need to apply the approximation formula: (Given number - smaller perfect square) ÷ (larger perfect square - smaller perfect square) Applying the formula: (9225 - 9216) ÷ (9409 - 9216) = 9 ÷ 193 ≈ 0.0466
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 96 + 0.0466 ≈ 96.0466, so the square root of 9225 is approximately 96.05.
Common Mistakes and How to Avoid Them in the Square Root of 9225
Students do make mistakes while finding the square root, such as forgetting about the negative square root or skipping steps in long division methods. 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 considering 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 the square root symbol in proper places
Not using the square root properly is another mistake that students make. To resolve this, we need to teach children that simplifying the numbers inside the square root is important before moving on to the second 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, resulting in a wrong answer at the end of the sum. This may either happen in subtracting or elsewhere.
Square Root of 9225 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √9225?
The area of the square is 9225 square units.
Explanation
The area of the square = side².
The side length is given as √9225.
Area of the square = side² = √9225 x √9225 = 96.06559 × 96.06559 ≈ 9225.
Therefore, the area of the square box is 9225 square units.
Problem 2
A square-shaped building measuring 9225 square feet is built; if each of the sides is √9225, what will be the square feet of half of the building?
4612.5 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 9225 by 2, we get 4612.5.
So half of the building measures 4612.5 square feet.
Problem 3
Calculate √9225 x 5.
480.32795
Explanation
The first step is to find the square root of 9225, which is approximately 96.06559.
The second step is to multiply 96.06559 with 5.
So 96.06559 x 5 ≈ 480.32795.
Problem 4
What will be the square root of (9216 + 9)?
The square root is 96.06559.
Explanation
To find the square root, we need to find the sum of (9216 + 9). 9216 + 9 = 9225, and then √9225 ≈ 96.06559.
Therefore, the square root of (9216 + 9) is approximately 96.06559.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √9225 units and the width ‘w’ is 25 units.
The perimeter of the rectangle is approximately 242.13118 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√9225 + 25) ≈ 2 × (96.06559 + 25) ≈ 2 × 121.06559 ≈ 242.13118 units.
FAQ on Square Root of 9225
1.What is √9225 in its simplest form?
2.Mention the factors of 9225.
3.Calculate the square of 9225.
4.Is 9225 a prime number?
5.9225 is divisible by?
6.How does learning Algebra help students in United Arab Emirates make better decisions in daily life?
7.How can cultural or local activities in United Arab Emirates support learning Algebra topics such as Square Root of 9225?
8.How do technology and digital tools in United Arab Emirates support learning Algebra and Square Root of 9225?
9.Does learning Algebra support future career opportunities for students in United Arab Emirates?
Important Glossaries for the Square Root of 9225
- 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 the positive square root that has more prominence due to its uses in the real world. That is the reason it is also known as the principal square root.
- Prime factorization: The process of expressing a number as a product of its prime factors.
- Long division method: A technique for finding the square root of a number through repeated division and approximation steps.
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About BrightChamps in United Arab Emirates
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.
