124 LearnersLast updated on May 26th, 2025
Square Root of 8825
If a number is multiplied by itself, the result is a square. The inverse of the square is a square root. The square root is used in various fields such as vehicle design, finance, etc. Here, we will discuss the square root of 8825.
What is the Square Root of 8825?
The square root is the inverse of the square of the number. 8825 is not a perfect square. The square root of 8825 is expressed in both radical and exponential form. In the radical form, it is expressed as √8825, whereas in the exponential form it is expressed as 8825^(1/2). √8825 ≈ 93.9685, 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 8825
The prime factorization method is used for perfect square numbers. However, for non-perfect square numbers, the long division method and approximation method are used. Let us now learn about the following methods:
- Prime factorization method
- Long division method
- Approximation method
Square Root of 8825 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 8825 is broken down into its prime factors.
Step 1: Finding the prime factors of 8825
Breaking it down, we get 5 x 5 x 7 x 13 x 19: 5^2 x 7 x 13 x 19
Step 2: Now we have found the prime factors of 8825. The second step is to make pairs of those prime factors. Since 8825 is not a perfect square, the digits of the number can’t be completely grouped in pairs. Therefore, calculating √8825 using prime factorization is not straightforward.
Square Root of 8825 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 8825, we need to group it as 88 and 25.
Step 2: Now we need to find n whose square is less than or equal to 88. We can say n is ‘9’ because 9 x 9 = 81 which is less than 88. Now the quotient is 9, after subtracting 81 from 88, the remainder is 7.
Step 3: Now let us bring down 25, which is 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 18_, and we need to find the value of n.
Step 5: The next step is finding 18n x n ≤ 725. Let us consider n as 4. Now, 184 x 4 = 736, which exceeds 725. Try n as 3. Now 183 x 3 = 549 which is less than 725.
Step 6: Subtract 549 from 725, the difference is 176, and the quotient is 93.
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 zeros to the dividend. Now the new dividend is 17600.
Step 8: Now we need to find the new divisor, which is 939. We need to find n such that 939n x n is closest to 17600.
Step 9: Continuing this process will give us the approximate value of the square root of 8825.
Square Root of 8825 by Approximation Method
The approximation method is another method for finding square roots. It is an easy method to estimate the square root of a given number. Now let us learn how to find the square root of 8825 using the approximation method.
Step 1: Now we have to find the closest perfect squares around √8825. The smallest perfect square less than 8825 is 8836, and the largest perfect square greater than 8825 is 8712. Therefore, √8825 falls somewhere between 93 and 94.
Step 2: Now we need to apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square) Going by the formula, (8825 - 8649) / (8836 - 8649) = 0.9685
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 93 + 0.9685 = 93.9685. Thus, the square root of 8825 is approximately 93.9685.
Common Mistakes and How to Avoid Them in the Square Root of 8825
Students often make mistakes while finding square roots, such as forgetting about the negative square root or skipping long division steps. 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 has both positive and negative square roots. However, we generally consider only the positive square root, as it is the required one in most practical scenarios.
For example: √50 = 7.071, but there is also -7.071 which should not be forgotten.
Mistake 2
Not adding the square root symbol in proper places
Not using the square root symbol properly is another mistake that students make. To resolve this, we need to teach students that simplifying the numbers inside the square root is important before moving on to further calculations.
For example: √(12 + 24) = √36, not √12 + √24.
Mistake 3
Not finding the correct value of a non-perfect square
The first step that needs to be taught to students is to simplify the numbers inside the square root. This ensures they do not make mistakes while identifying the approximate value.
For example, √50 ≠ 7; 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 cube root and square root consistently, as this will help them avoid confusion.
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. This may occur during subtraction or elsewhere in the process.
Square Root of 8825 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √8825?
The area of the square is 8825 square units.
Explanation
The area of the square = side^2.
The side length is given as √8825.
Area of the square = (√8825)^2 = 8825.
Therefore, the area of the square box is 8825 square units.
Problem 2
A square-shaped building measuring 8825 square feet is built; if each of the sides is √8825, what will be the square feet of half of the building?
4412.5 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 8825 by 2 = 4412.5.
So half of the building measures 4412.5 square feet.
Problem 3
Calculate √8825 x 5.
469.8425
Explanation
The first step is to find the square root of 8825, which is approximately 93.9685.
The second step is to multiply 93.9685 by 5.
So, 93.9685 x 5 ≈ 469.8425.
Problem 4
What will be the square root of (8825 + 25)?
The square root is 95.
Explanation
To find the square root, we need to find the sum of (8825 + 25). 8825 + 25 = 8850, and then √8850 ≈ 94.12.
Therefore, the square root of (8825 + 25) is approximately 94.12.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √8825 units and the width ‘w’ is 50 units.
The perimeter of the rectangle is approximately 387.937 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√8825 + 50) = 2 × (93.9685 + 50) ≈ 2 × 143.9685 = 287.937 units.
FAQ on Square Root of 8825
1.What is √8825 in its simplest form?
2.Mention the factors of 8825.
3.Calculate the square of 8825.
4.Is 8825 a prime number?
5.8825 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 8825?
8.How do technology and digital tools in Australia support learning Algebra and Square Root of 8825?
9.Does learning Algebra support future career opportunities for students in Australia?
Important Glossaries for the Square Root of 8825
- Square root: A square root is the inverse operation of squaring a number. For example, 4^2 = 16, and the square root is √16 = 4.
- Irrational number: An irrational number cannot be expressed in the form of p/q, where p and q are integers and q ≠ 0.
- Long division method: A method used for finding the square roots of non-perfect squares through a systematic approach of division.
- Approximation: A method of estimating a value between two known values.
- Decimal: A number that includes a whole number and a fractional part, represented with a decimal point, such as 7.86, 8.65, and 9.42.
Explore More algebra
About BrightChamps in Australia
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.
