Square Root of 10025
2026-02-28 17:33 Diff
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Last updated on August 5, 2025

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 10025.

What is the Square Root of 10025?

The square root is the inverse of the square of the number. 10025 is not a perfect square. The square root of 10025 is expressed in both radical and exponential form. In radical form, it is expressed as √10025, whereas (10025)^(1/2) in exponential form. √10025 ≈ 100.1249, 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 10025

The prime factorization method is used for perfect square numbers. However, for non-perfect square numbers, the prime factorization method is not used; instead, 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 10025 by Prime Factorization Method

The product of prime factors is the prime factorization of a number. Now let us look at how 10025 is broken down into its prime factors.

Step 1: Finding the prime factors of 10025

Breaking it down, we get 5 x 5 x 401.

Step 2: Now we found out the prime factors of 10025. The second step is to make pairs of those prime factors. Since 10025 is not a perfect square, the digits of the number can’t be grouped in pairs. Therefore, calculating 10025 using prime factorization alone is not straightforward, and approximation or other methods are more useful.

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Square Root of 10025 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, group the numbers from right to left. In the case of 10025, group it as 25 and 100.

Step 2: Find a number whose square is less than or equal to 100. The number is 10 because 10 x 10 = 100. Now, the quotient is 10, and the remainder is 0.

Step 3: Bring down 25, which is the new dividend. Add the old divisor with the same number, 10 + 10, to get 20 as the new divisor.

Step 4: Find n such that 20n x n ≤ 25. Let n be 0, so 20 x 0 = 0.

Step 5: Subtract 0 from 25, the difference is 25, and the quotient is 100.

Step 6: Since the dividend is less than the divisor, add a decimal point. Adding the decimal allows us to add two zeros to the dividend. Now the dividend is 2500.

Step 7: Find the new divisor that is 2002 because 2002 x 1 = 2002.

Step 8: Subtract 2002 from 2500 to get 498.

Step 9: Continue these steps until the desired accuracy is achieved.

Eventually, the square root of 10025 ≈ 100.1249.

Square Root of 10025 by Approximation Method

The approximation method is another method for finding square roots, and it is an easy method for estimating the square root of a given number. Now let us learn how to find the square root of 10025 using the approximation method.

Step 1: Find the closest perfect squares to √10025. The smallest perfect square less than 10025 is 10000 (100^2), and the largest perfect square greater than 10025 is 10201 (101^2). √10025 falls somewhere between 100 and 101.

Step 2: Apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square) (10025 - 10000) / (10201 - 10000) = 25 / 201 ≈ 0.1249

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 + 0.1249 = 100.1249. So the square root of 10025 is approximately 100.1249.

Common Mistakes and How to Avoid Them in the Square Root of 10025

Students do make mistakes while finding square roots, such as forgetting about the negative square root and skipping steps in the long division method. Let us look at some mistakes that students tend to make in detail.

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Problem 1

Can you help Max find the area of a square box if its side length is given as √10025?

Okay, lets begin

The area of the square is approximately 10025 square units.

Explanation

The area of the square = side^2.

The side length is given as √10025.

Area of the square = side^2 = √10025 x √10025 = 10025.

Therefore, the area of the square box is approximately 10025 square units.

Well explained 👍

Problem 2

A square-shaped building measuring 10025 square feet is built; if each of the sides is √10025, what will be the square feet of half of the building?

Okay, lets begin

5012.5 square feet

Explanation

We can divide the given area by 2 as the building is square-shaped.

Dividing 10025 by 2 gives us 5012.5.

So half of the building measures 5012.5 square feet.

Well explained 👍

Problem 3

Calculate √10025 x 5.

Okay, lets begin

Approximately 500.6245

Explanation

First, find the square root of 10025, which is approximately 100.1249.

The second step is to multiply 100.1249 by 5.

So, 100.1249 x 5 ≈ 500.6245.

Well explained 👍

Problem 4

What will be the square root of (10000 + 25)?

Okay, lets begin

The square root is approximately 100.1249

Explanation

To find the square root, sum (10000 + 25). 10000 + 25 = 10025, and then √10025 ≈ 100.1249.

Therefore, the square root of (10000 + 25) is approximately 100.1249.

Well explained 👍

Problem 5

Find the perimeter of the rectangle if its length ‘l’ is √10025 units and the width ‘w’ is 38 units.

Okay, lets begin

The perimeter of the rectangle is approximately 276.2498 units.

Explanation

Perimeter of the rectangle = 2 × (length + width)

Perimeter = 2 × (√10025 + 38) = 2 × (100.1249 + 38) = 2 × 138.1249 ≈ 276.2498 units.

Well explained 👍

FAQ on Square Root of 10025

1.What is √10025 in its simplest form?

The simplest form of √10025, given that it involves a non-perfect square, is approximately 100.1249.

2.Mention the factors of 10025.

Factors of 10025 include 1, 5, 25, 401, 2005, and 10025.

3.Calculate the square of 10025.

We get the square of 10025 by multiplying the number by itself, that is 10025 x 10025 = 100500625.

4.Is 10025 a prime number?

10025 is not a prime number, as it has more than two factors.

5.10025 is divisible by?

10025 is divisible by 1, 5, 25, 401, 2005, and 10025.

Important Glossaries for the Square Root of 10025

  • Square root: A square root is the inverse of a square. For example, 10^2 = 100, and the inverse of the square is the square root, that is, √100 = 10.
     
  • Irrational number: An irrational number 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, the positive square root, known as the principal square root, is often used due to its practical applications.
     
  • Factors: Factors are numbers that divide another number completely without leaving a remainder.
     
  • Approximation: Approximation involves estimating the value of a number or expression based on close or nearby values.

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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

: He loves to play the quiz with kids through algebra to make kids love it.