126 LearnersLast updated on May 26th, 2025
Square Root of 10125
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 10125.
What is the Square Root of 10125?
The square root is the inverse of the square of the number. 10125 is not a perfect square. The square root of 10125 is expressed in both radical and exponential forms. In the radical form, it is expressed as √10125, whereas in exponential form it is expressed as (10125)^(1/2). √10125 = 100.622, 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 10125
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 10125 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 10125 is broken down into its prime factors:
Step 1: Finding the prime factors of 10125
Breaking it down, we get 3 x 3 x 3 x 3 x 5 x 5 x 5: 3^4 x 5^3
Step 2: Now we found out the prime factors of 10125. The second step is to make pairs of those prime factors. Since 10125 is not a perfect square, the digits of the number can’t be grouped in pairs completely. Therefore, calculating 10125 using prime factorization does not yield an integer result.
Square Root of 10125 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 10125, we need to group it as 25, 01, and 10.
Step 2: Now we need to find n whose square is lesser than or equal to 10. We can say n as ‘3’ because 3 x 3 = 9 is lesser than or equal to 10. Now the quotient is 3, after subtracting 9 from 10 the remainder is 1.
Step 3: Now let us bring down 01 to make it 101. Add the old divisor with the same number 3 + 3 = 6, which will be our new divisor.
Step 4: The new divisor will be the sum of the dividend and quotient. Now we get 6n as the new divisor, we need to find the value of n.
Step 5: The next step is finding 6n x n ≤ 101, let us consider n as 1, now 61 x 1 = 61.
Step 6: Subtract 61 from 101; the difference is 40, and the quotient is 31.
Step 7: Bring down the next pair, 25, making the new dividend 4025.
Step 8: Add a decimal point after the quotient. Now, find the new divisor as 622 because 622 x 6 = 3732.
Step 9: Subtracting 3732 from 4025, we get 293.
Step 10: Continue these steps until we get two numbers after the decimal point. Suppose if there is no decimal value, continue till the remainder is zero.
So the square root of √10125 is approximately 100.62.
Square Root of 10125 by Approximation Method
The approximation method is another method for finding square roots, and 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 10125 using the approximation method.
Step 1: Now we have to find the closest perfect square of √10125. The smallest perfect square less than 10125 is 10000 and the largest perfect square more than 10125 is 10404. √10125 falls somewhere between 100 and 102.
Step 2: Now we need to apply the formula that is (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Going by the formula (10125 - 10000) ÷ (10404 - 10000) = 0.625.
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 100 + 0.62 = 100.62, so the square root of 10125 is approximately 100.62.
Common Mistakes and How to Avoid Them in the Square Root of 10125
Students make mistakes while finding the square root, such as 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 has both positive and negative square roots. However, we typically consider only the principal (positive) square root, as it is the required one in most contexts.
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 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: √(12+24) = √12 + √24 is the 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 = 7.071067.
Mistake 4
Confusing the square root symbol with the cube root
Students need to be taught the difference between cube root and square root 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 subtraction or elsewhere.
Square Root of 10125 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √10125?
The area of the square is 10125 square units.
Explanation
The area of the square = side².
The side length is given as √10125.
Area of the square = side² = √10125 x √10125 = 10125.
Therefore, the area of the square box is 10125 square units.
Problem 2
A square-shaped building measuring 10125 square feet is built; if each of the sides is √10125, what will be the square feet of half of the building?
5062.5 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 10125 by 2 = we get 5062.5.
So half of the building measures 5062.5 square feet.
Problem 3
Calculate √10125 x 5.
503.11
Explanation
The first step is to find the square root of 10125, which is approximately 100.62.
The second step is to multiply 100.62 by 5.
So 100.62 x 5 = 503.11.
Problem 4
What will be the square root of (10125 + 100)?
The square root is approximately 101.12.
Explanation
To find the square root, we need to find the sum of (10125 + 100). 10125 + 100 = 10225, and then √10225 ≈ 101.12.
Therefore, the square root of (10125 + 100) is approximately ±101.12.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √10125 units and the width ‘w’ is 50 units.
The perimeter of the rectangle is approximately 301.24 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√10125 + 50) = 2 × (100.62 + 50) = 2 × 150.62 = 301.24 units.
FAQ on Square Root of 10125
1.What is √10125 in its simplest form?
2.Mention the factors of 10125.
3.Calculate the square of 10125.
4.Is 10125 a prime number?
5.10125 is divisible by?
6.How does learning Algebra help students in Qatar make better decisions in daily life?
7.How can cultural or local activities in Qatar support learning Algebra topics such as Square Root of 10125?
8.How do technology and digital tools in Qatar support learning Algebra and Square Root of 10125?
9.Does learning Algebra support future career opportunities for students in Qatar?
Important Glossaries for the Square Root of 10125
- Square root: A square root is the inverse of the 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: Prime factorization is the process of expressing a number as the product of its prime numbers.
- Long division method: A method used to find the square root of non-perfect square numbers through a series of division steps to achieve an approximation.
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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
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