138 LearnersLast updated on May 26th, 2025
Square Root of 11025
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 11025.
What is the Square Root of 11025?
The square root is the inverse of the square of the number. 11025 is a perfect square. The square root of 11025 is expressed in both radical and exponential form. In the radical form, it is expressed as √11025, whereas (11025)^(1/2) in the exponential form. √11025 = 105, which is a rational number because it can be expressed in the form of p/q, where p and q are integers and q ≠ 0.
Finding the Square Root of 11025
The prime factorization method is used for perfect square numbers. For perfect squares like 11025, the prime factorization method is very effective. Let us now learn the following methods:
- Prime factorization method
- Long division method
- Approximation method
Square Root of 11025 by Prime Factorization Method
The product of prime factors is the Prime factorization of a number. Now let us look at how 11025 is broken down into its prime factors.
Step 1: Finding the prime factors of 11025
Breaking it down, we get 3 x 3 x 5 x 5 x 7 x 7: 3^2 x 5^2 x 7^2
Step 2: Now we found out the prime factors of 11025. The second step is to make pairs of those prime factors. Since 11025 is a perfect square, we can make pairs of each prime factor: (3 x 3), (5 x 5), and (7 x 7). The square root of 11025 is the product of one factor from each pair, which is 3 x 5 x 7 = 105.
Square Root of 11025 by Long Division Method
The long division method can also be used for perfect squares. 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 11025, we need to group it as 25 and 110.
Step 2: Now we need to find n whose square is less than or equal to 11. We can say n as ‘3’ because 3 x 3 = 9 is lesser than or equal to 11. Now the quotient is 3, and after subtracting 9 from 11, the remainder is 2.
Step 3: Now let us bring down 02, making the new dividend 202. Add the old divisor with the same number 3 + 3 to get 6, which will be our new divisor.
Step 4: The new divisor will be the sum of the dividend and quotient. Now we have 6n as the new divisor, and we need to find the value of n such that 60n x n ≤ 202
Step 5: Considering n as 3, we have 63 x 3 = 189.
Step 6: Subtract 189 from 202, the difference is 13, and the quotient is 33.
Step 7: Bring down 25, making the new dividend 1325. Add a decimal point to the quotient.
Step 8: The new divisor will be 660. Finding n such that 660n x n ≤ 1325, we get n = 2.
Step 9: The remainder becomes 0 after subtracting, and the quotient is 105.
Square Root of 11025 by Approximation Method
The approximation method is another method for finding the square roots, but for a perfect square like 11025, the exact method is more appropriate. Now let us learn how to find the square root of 11025 using approximation.
Step 1: Now we have to find the closest perfect square of √11025. The closest perfect squares around 11025 are 10816 (104^2) and 11236 (106^2). √11025 falls exactly at 105, which is between 104 and 106.
Step 2: The square root of 11025 is precisely 105.
Common Mistakes and How to Avoid Them in the Square Root of 11025
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: √11025 = 105, there is also -105 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: √(25+10000) = √25 + √10000 is the wrong method of using roots. The right way of using roots is √(25+10000) = √10025.
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: √11025 = 106 is wrong, the correct answer is √11025 = 105.
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 keep away from mistakes.
For Example: √11025 and ∛11025 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 11025 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √11025?
The area of the square is 11025 square units.
Explanation
The area of the square = side^2.
The side length is given as √11025.
Area of the square = side^2 = 105 x 105 = 11025
Therefore, the area of the square box is 11025 square units.
Problem 2
A square-shaped building measuring 11025 square feet is built; if each of the sides is √11025, what will be the square feet of half of the building?
5512.5 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 11025 by 2 = we get 5512.5
So half of the building measures 5512.5 square feet.
Problem 3
Calculate √11025 x 5.
525
Explanation
The first step is to find the square root of 11025, which is 105.
The second step is to multiply 105 with 5.
So 105 x 5 = 525.
Problem 4
What will be the square root of (11025 + 0)?
The square root is 105.
Explanation
To find the square root, we need to find the sum of (11025 + 0). 11025 + 0 = 11025, and then √11025 = 105.
Therefore, the square root of (11025 + 0) is ±105.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √11025 units and the width ‘w’ is 50 units.
We find the perimeter of the rectangle as 310 units.
Explanation
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√11025 + 50) = 2 × (105 + 50) = 2 × 155 = 310 units.
FAQ on Square Root of 11025
1.What is √11025 in its simplest form?
2.Mention the factors of 11025.
3.Calculate the square of 105.
4.Is 11025 a prime number?
5.11025 is divisible by?
6.How does learning Algebra help students in Oman make better decisions in daily life?
7.How can cultural or local activities in Oman support learning Algebra topics such as Square Root of 11025?
8.How do technology and digital tools in Oman support learning Algebra and Square Root of 11025?
9.Does learning Algebra support future career opportunities for students in Oman?
Important Glossaries for the Square Root of 11025
- Square root: A square root is the inverse of a square. Example: 10^2 = 100 and the inverse of the square is the square root, that is, √100 = 10.
- Rational number: A rational number is a number that can 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. Example: 144 is a perfect square since it is 12^2.
- Prime factorization: Prime factorization is the process of expressing a number as a product of its prime factors. For example, the prime factorization of 28 is 2 x 2 x 7.
- Long division method: A method used to find the square root of a number by grouping digits, finding divisors, and calculating remainders systematically.
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About BrightChamps in Oman
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.
