Square Root of 15625
2026-02-28 09:11 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 15625.

What is the Square Root of 15625?

The square root is the inverse of the square of a number. 15625 is a perfect square. The square root of 15625 is expressed in both radical and exponential form. In the radical form, it is expressed as √15625, whereas (15625)(1/2) in the exponential form. √15625 = 125, 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 15625

The prime factorization method is used for perfect square numbers. The long-division method and approximation method can also be used for verification. Let us now learn the following methods:

  1. Prime factorization method
  2. Long division method
  3. Approximation method

Square Root of 15625 by Prime Factorization Method

The product of prime factors is the prime factorization of a number. Now let us look at how 15625 is broken down into its prime factors.

Step 1: Finding the prime factors of 15625 Breaking it down, we get 5 x 5 x 5 x 5 x 5 x 5: 56

Step 2: Now we found the prime factors of 15625. The second step is to make pairs of those prime factors. Since 15625 is a perfect square, the digits of the number can be grouped in pairs.

Step 3: Taking one number from each pair gives us the square root: 5 x 5 x 5 = 125

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Square Root of 15625 by Long Division Method

The long division method can be used to find the square root of perfect square numbers. 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 15625, we need to group it as 15 625.

Step 2: Now we need to find n whose square is less than or equal to 15. We can say n is 3 because 32 = 9, which is less than 15. Now the quotient is 3, and the remainder is 15 - 9 = 6.

Step 3: Bring down the next pair of digits, 62, making the new dividend 662.

Step 4: Double the quotient and find the new divisor. The current quotient is 3, so doubling it gives us 6.

Step 5: We try 65 as the new divisor since 65 x 5 = 325, which is less than 662. The remainder is 662 - 325 = 337.

Step 6: Bring down the next pair of digits, 25, making the new dividend 33725.

Step 7: Double the current quotient (35) gives us 70. Step 8: Try 705 as the new divisor since 705 x 5 = 3525, which is less than 33725.

Step 9: The remainder is 33725 - 3525 = 0. So the square root of √15625 is 125.

Square Root of 15625 by Approximation Method

Approximation method is an easy way to find the square root of a given number. Now let us learn how to find the square root of 15625 using the approximation method.

Step 1: Now we have to find the closest perfect square of √15625. Since 15625 is a perfect square, the square root is an integer.

Step 2: The square root is exactly 125, as calculated by methods above.

Common Mistakes and How to Avoid Them in the Square Root of 15625

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.

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Problem 1

Can you help Max find the area of a square box if its side length is given as √15625?

Okay, lets begin

The area of the square is 15625 square units.

Explanation

The area of the square = side2.

The side length is given as √15625.

Area of the square = side2 = (√15625)2 = 125 x 125 = 15625.

Therefore, the area of the square box is 15625 square units.

Well explained 👍

Problem 2

A square-shaped building measuring 15625 square feet is built; if each of the sides is √15625, what will be the square feet of half of the building?

Okay, lets begin

7812.5 square feet

Explanation

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

Dividing 15625 by 2 = we get 7812.5

So half of the building measures 7812.5 square feet.

Well explained 👍

Problem 3

Calculate √15625 x 5.

Okay, lets begin

625

Explanation

The first step is to find the square root of 15625, which is 125.

The second step is to multiply 125 with 5.

So 125 x 5 = 625.

Well explained 👍

Problem 4

What will be the square root of (14400 + 1225)?

Okay, lets begin

The square root is 125.

Explanation

To find the square root, we need to find the sum of (14400 + 1225). 14400 + 1225 = 15625, and then √15625 = 125.

Therefore, the square root of (14400 + 1225) is ±125.

Well explained 👍

Problem 5

Find the perimeter of the rectangle if its length ‘l’ is √15625 units and the width ‘w’ is 50 units.

Okay, lets begin

We find the perimeter of the rectangle as 350 units.

Explanation

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

Perimeter = 2 × (√15625 + 50) = 2 × (125 + 50) = 2 × 175 = 350 units.

Well explained 👍

FAQ on Square Root of 15625

1.What is √15625 in its simplest form?

The prime factorization of 15625 is 5 x 5 x 5 x 5 x 5 x 5, so the simplest form of √15625 = 5 x 5 x 5 = 125.

2.Mention the factors of 15625.

Factors of 15625 are 1, 5, 25, 125, 625, 3125, and 15625.

3.Calculate the square of 15625.

We get the square of 15625 by multiplying the number by itself, that is 15625 x 15625 = 244140625.

4.Is 15625 a prime number?

15625 is not a prime number, as it has more than two factors.

5.15625 is divisible by?

15625 has factors that include 1, 5, 25, 125, 625, 3125, and 15625.

Important Glossaries for the Square Root of 15625

  • 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.
  • 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.
  • 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.
  • Perfect square: A perfect square is a number that is the square of an integer. Example: 16 is a perfect square since it is 42.
  • Prime factorization: Prime factorization is expressing a number as the product of its prime factors. Example: 15625 = 5^6.

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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.