Square Root of 10625
2026-02-28 17:37 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-10625

287 Learners

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 fields such as vehicle design, finance, etc. Here, we will discuss the square root of 10625.

What is the Square Root of 10625?

The square root is the inverse of the square of a number. 10625 is a perfect square. The square root of 10625 is expressed in both radical and exponential form. In the radical form, it is expressed as √10625, whereas (10625)^(1/2) in the exponential form. √10625 = 103, 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 10625

The prime factorization method is used for perfect square numbers. Let us now learn the following methods:

  • Prime factorization method
  • Long division method

Square Root of 10625 by Prime Factorization Method

The product of prime factors is the prime factorization of a number. Now let us look at how 10625 is broken down into its prime factors.

Step 1: Finding the prime factors of 10625

Breaking it down, we get 5 x 5 x 5 x 5 x 17: 5^4 x 17^1

Step 2: Now that we found out the prime factors of 10625, the second step is to make pairs of those prime factors. Since 10625 is a perfect square, prime factors can be paired: (5 x 5), (5 x 5). Therefore, calculating 10625 using prime factorization gives us 103.

Explore Our Programs

Square Root of 10625 by Long Division Method

The long division method is particularly used for non-perfect square numbers, but it can also be used for perfect squares. 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 10625, we group it as 25 and 106.

Step 2: Now, we need to find n whose square is less than or equal to 106. We can say n is ‘10’ because 10 x 10 = 100, which is less than 106. Now the quotient is 10, after subtracting 106 - 100, the remainder is 6.

Step 3: Bring down 25 to make the new dividend 625.

Step 4: The new divisor will be the sum of the old divisor and the quotient, so 10 + 10 = 20.

Step 5: We need to find n such that 20n x n ≤ 625. Let us consider n as 3. Now, 203 x 3 = 609.

Step 6: Subtract 625 from 609, the difference is 16, and the quotient is 103.

Step 7: Since there is no remainder, the process stops here, confirming that the square root of 10625 is 103.

Download Worksheets

Problem 1

Can you help Max find the area of a square box if its side length is given as √10625?

Okay, lets begin

The area of the square is 10625 square units.

Explanation

The area of the square = side^2.

The side length is given as √10625.

Area of the square = side^2 = √10625 x √10625 = 103 x 103 = 10625

Therefore, the area of the square box is 10625 square units.

Well explained 👍

Problem 2

A square-shaped building measuring 10625 square feet is built; if each of the sides is √10625, what will be the square feet of half of the building?

Okay, lets begin

5312.5 square feet

Explanation

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

Dividing 10625 by 2 = we get 5312.5

So half of the building measures 5312.5 square feet.

Well explained 👍

Problem 3

Calculate √10625 x 5.

Okay, lets begin

515

Explanation

The first step is to find the square root of 10625, which is 103.

The second step is to multiply 103 by 5.

So 103 x 5 = 515.

Well explained 👍

Problem 4

What will be the square root of (10000 + 625)?

Okay, lets begin

The square root is 103

Explanation

To find the square root, we need to find the sum of (10000 + 625). 10000 + 625 = 10625, and then √10625 = 103.

Therefore, the square root of (10000 + 625) is ±103.

Well explained 👍

Problem 5

Find the perimeter of the rectangle if its length ‘l’ is √10625 units and the width ‘w’ is 38 units.

Okay, lets begin

We find the perimeter of the rectangle as 282 units.

Explanation

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

Perimeter = 2 × (√10625 + 38) = 2 × (103 + 38) = 2 × 141 = 282 units.

Well explained 👍

FAQ on Square Root of 10625

1.What is √10625 in its simplest form?

The prime factorization of 10625 is 5 x 5 x 5 x 5 x 17, so the simplest form of √10625 = √(5^4 x 17) = 103.

2.Mention the factors of 10625.

Factors of 10625 are 1, 5, 25, 125, 425, 2125, 10625.

3.Calculate the square of 10625.

We get the square of 103 by multiplying the number by itself, that is 103 x 103 = 10609.

4.Is 10625 a prime number?

10625 is not a prime number, as it has more than two factors.

5.10625 is divisible by?

10625 has factors; those are 1, 5, 25, 125, 425, 2125, 10625.

Important Glossaries for the Square Root of 10625

  • Square root: A square root is the inverse of a square. Example: 4^2 = 16 and the inverse of the square is the square root, that is √16 = 4.
     
  • 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. For example, 4, 9, and 16 are perfect squares.
     
  • Prime factorization: Prime factorization is expressing a number as the product of its prime factors.
     
  • Long division method: A systematic method to find the square root of a number, especially useful for large numbers or non-perfect squares.

What Is Algebra? 🧮 | Simple Explanation with 🎯 Cool Examples for Kids | ✨BrightCHAMPS Math

▶

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.