103 LearnersLast updated on May 26th, 2025
Square Root of 11250
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 11250.
What is the Square Root of 11250?
The square root is the inverse of the square of the number. 11250 is not a perfect square. The square root of 11250 is expressed in both radical and exponential form. In the radical form, it is expressed as √11250, whereas (11250)¹/² in the exponential form. √11250 ≈ 106.066, 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 11250
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 the following methods:
- Prime factorization method
- Long division method
- Approximation method
Square Root of 11250 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 11250 is broken down into its prime factors.
Step 1: Finding the prime factors of 11250
Breaking it down, we get 2 x 3 x 3 x 5 x 5 x 5 x 5: 2¹ x 3² x 5⁴
Step 2: Now we found out the prime factors of 11250. The second step is to make pairs of those prime factors. Since 11250 is not a perfect square, the digits of the number can’t be grouped in pairs completely. Therefore, calculating 11250 using prime factorization directly is not possible.
Square Root of 11250 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 11250, we need to group it as 50, 12, and 11.
Step 2: Now we need to find n whose square is ≤ 11. We can say n is ‘3’ because 3 x 3 = 9, which is less than 11. Now the quotient is 3, and the remainder is 2.
Step 3: Now let us bring down 1250, which is the new dividend. Add the old divisor with the same number 3 + 3, we get 6, which will be our new divisor's starting digit.
Step 4: The new divisor will be 60n. We need to find the value of n.
Step 5: The next step is finding the largest digit n such that 60n x n ≤ 225. Let us consider n as 3, now 63 x 3 = 189.
Step 6: Subtract 189 from 225, the difference is 36. Bring down the next pair of zeros to make it 3600.
Step 7: The process continues, finding n for 606n ≤ 3600, which would be n = 5, making the next number 65.
Step 8: Repeat these steps to find the decimal places.
So the square root of √11250 ≈ 106.066.
Square Root of 11250 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 11250 using the approximation method.
Step 1: Now we have to find the closest perfect square of √11250. The smallest perfect square less than 11250 is 11025, and the largest perfect square more than 11250 is 11664. √11250 falls between 105 and 108.
Step 2: Now we need to apply the formula that is (Given number - smallest perfect square) ÷ (Greater perfect square - smallest perfect square). Using the formula (11250 - 11025) ÷ (11664 - 11025) = 0.225.
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 105 + 0.225 = 105.225. Therefore, the square root of 11250 is approximately 106.066, after further refinement.
Common Mistakes and How to Avoid Them in the Square Root of 11250
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, √11250 ≈ 106.066, there is also -106.066 which should not be forgotten.
Square root of 11250 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √112?
The area of the square is approximately 1254.24 square units.
Explanation
The area of the square = side².
The side length is given as √112.
Area of the square = side² = √112 x √112 ≈ 10.583 x 10.583 = 1254.24
Therefore, the area of the square box is approximately 1254.24 square units.
Problem 2
A square-shaped building measuring 11250 square feet is built; if each of the sides is √11250, what will be the square feet of half of the building?
5625 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 11250 by 2 = we get 5625.
So half of the building measures 5625 square feet.
Problem 3
Calculate √11250 x 5.
530.33
Explanation
The first step is to find the square root of 11250, which is approximately 106.066.
The second step is to multiply 106.066 by 5.
So 106.066 x 5 ≈ 530.33.
Problem 4
What will be the square root of (11025 + 225)?
The square root is 108.
Explanation
To find the square root, we need to find the sum of (11025 + 225). 11025 + 225 = 11250, and then √11250 ≈ 106.066.
Therefore, the square root of (11025 + 225) is approximately 106.066.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √112 units and the width ‘w’ is 38 units.
We find the perimeter of the rectangle as approximately 97.166 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√112 + 38) ≈ 2 × (10.583 + 38) = 2 × 48.583 = 97.166 units.
FAQ on Square Root of 11250
1.What is √11250 in its simplest form?
2.Mention the factors of 11250.
3.Calculate the square of 11250.
4.Is 11250 a prime number?
5.11250 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 11250?
8.How do technology and digital tools in Singapore support learning Algebra and Square Root of 11250?
9.Does learning Algebra support future career opportunities for students in Singapore?
Important Glossaries for the Square Root of 11250
- 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 a principal square root.
- Prime factorization: The process of breaking down a composite number into its prime factors. For example, the prime factorization of 11250 is 2 x 3² x 5⁴.
- Approximation: The method of finding a value that is close enough to the correct value, usually within an acceptable error margin.
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About BrightChamps in Singapore
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.
