102 LearnersLast updated on May 26th, 2025
Square Root of 8800
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 8800.
What is the Square Root of 8800?
The square root is the inverse of the square of the number. 8800 is not a perfect square. The square root of 8800 is expressed in both radical and exponential form. In the radical form, it is expressed as √8800, whereas (8800)^(1/2) in the exponential form. √8800 ≈ 93.808, 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 8800
The prime factorization method is often used for perfect square numbers. However, for non-perfect square numbers like 8800, the long-division method and approximation method are typically used. Let us now learn the following methods:
Prime factorization method
- Long division method
- Approximation method
Square Root of 8800 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now, let us look at how 8800 is broken down into its prime factors.
Step 1: Finding the prime factors of 8800
Breaking it down, we get 2 x 2 x 2 x 2 x 5 x 5 x 11: 2^4 x 5^2 x 11
Step 2: We found the prime factors of 8800. The second step is to make pairs of those prime factors. Since 8800 is not a perfect square, the digits of the number can’t be grouped into pairs for all factors. Therefore, calculating 8800 using prime factorization directly to get a perfect square is impossible.
Square Root of 8800 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 8800, we need to group it as 88 and 00.
Step 2: Now, we need to find n whose square is ≤ 88. We can say n is ‘9’ because 9 x 9 = 81, which is less than 88. The quotient is 9, and after subtracting, the remainder is 7.
Step 3: Now, let us bring down 00, 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: We need to find n such that 18n × n ≤ 700. Let us consider n as 3, so 183 x 3 = 549.
Step 5: Subtract 549 from 700, and the difference is 151. The quotient is now 93.
Step 6: 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 15100.
Step 7: Now, we need to find the new divisor, which is 938, because 938 x 8 = 15008.
Step 8: Subtracting 15008 from 15100 gives us the result 92.
Step 9: Now the quotient is 93.8.
Step 10: Continue doing these steps until we get two numbers after the decimal point. If there are no decimal values, continue until the remainder is zero.
So the square root of √8800 ≈ 93.80
Square Root of 8800 by Approximation Method
The approximation method is another method for finding 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 8800 using the approximation method.
Step 1: First, find the closest perfect squares to √8800. The smallest perfect square less than 8800 is 8649, and the next perfect square greater than 8800 is 8836. √8800 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).
Using the formula: (8800 - 8649) / (8836 - 8649) = 151 / 187. This gives approximately 0.808. Adding the whole part gives us 93 + 0.808 = 93.808. So the square root of 8800 ≈ 93.808.
Common Mistakes and How to Avoid Them in the Square Root of 8800
Students often make mistakes while finding square roots, such as forgetting about the negative square root, skipping steps in the long division method, etc. Let us look at a few of these mistakes and how to avoid them.
Mistake 1
Forgetting about the Negative Square Root
It is important to remember that a number has both positive and negative square roots. However, we typically consider only the positive square root, as it is the required one in most applications.
For example: √50 ≈ 7.07, but there is also -7.07, which should not be forgotten.
Square Root of 8800 Examples
Problem 1
Can you help Sam find the area of a square box if its side length is given as √8800?
The area of the square is approximately 8800 square units.
Explanation
The area of a square = side^2.
The side length is given as √8800.
Area of the square = side^2 = √8800 x √8800 = 8800.
Therefore, the area of the square box is approximately 8800 square units.
Problem 2
A square-shaped garden measuring 8800 square feet is built; if each of the sides is √8800, what will be the square feet of half of the garden?
4400 square feet
Explanation
Simply divide the given area by 2 as the garden is square-shaped.
Dividing 8800 by 2, we get 4400.
So half of the garden measures 4400 square feet.
Problem 3
Calculate √8800 x 3.
281.424
Explanation
First, find the square root of 8800, which is approximately 93.808.
Then multiply 93.808 by 3.
So 93.808 x 3 ≈ 281.424.
Problem 4
What will be the square root of (8800 + 200)?
The square root is approximately 98.9949.
Explanation
To find the square root, we need to find the sum of (8800 + 200). 8800 + 200 = 9000, and then √9000 ≈ 94.8683.
Therefore, the square root of (8800 + 200) is approximately 94.8683.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √8800 units and the width ‘w’ is 50 units.
The perimeter of the rectangle is approximately 287.616 units.
Explanation
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√8800 + 50) = 2 × (93.808 + 50) = 2 × 143.808 = 287.616 units.
FAQ on Square Root of 8800
1.What is √8800 in its simplest form?
2.Mention the factors of 8800.
3.Calculate the square of 8800.
4.Is 8800 a prime number?
5.8800 is divisible by?
6.How does learning Algebra help students in United States make better decisions in daily life?
7.How can cultural or local activities in United States support learning Algebra topics such as Square Root of 8800?
8.How do technology and digital tools in United States support learning Algebra and Square Root of 8800?
9.Does learning Algebra support future career opportunities for students in United States?
Important Glossaries for the Square Root of 8800
- Square root: A square root is the inverse of a square. For 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.
- Perfect square: A perfect square is a number that is the square of an integer. For example, 49 is a perfect square since it is 7 squared.
- Long division method: A technique used to find the square root of non-perfect squares by dividing the number into parts.
- Prime factorization: This method involves expressing a number as the product of its prime factors.
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Jaskaran Singh Saluja
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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.
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