Square Root of 1225
2026-02-28 12:49 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 1225.

What is the Square Root of 1225?

The square root is the inverse of the square of the number. 1225 is a perfect square. The square root of 1225 is expressed in both radical and exponential forms. In the radical form, it is expressed as √1225, whereas (1225)^(1/2) in the exponential form. √1225 = 35, 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 1225

The prime factorization method is typically used for perfect square numbers like 1225. The long division method and approximation method are more suited for non-perfect square numbers. Let us now learn the following method:

Prime factorization method

Square Root of 1225 by Prime Factorization Method

The product of prime factors is the prime factorization of a number. Now let us look at how 1225 is broken down into its prime factors.

Step 1: Finding the prime factors of 1225 Breaking it down, we get 5 x 5 x 7 x 7: 5^2 x 7^2 Step 2: Now we found out the prime factors of 1225. The second step is to make pairs of those prime factors. Since 1225 is a perfect square, the digits of the number can be grouped into pairs.

Therefore, calculating √1225 using prime factorization gives us 5 x 7 = 35.

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Square Root of 1225 by Long Division Method

The long division method is generally used for non-perfect square numbers but can be demonstrated for perfect squares like 1225 for practice. In this method, we verify that our calculation matches the known perfect square root.

Step 1: To begin with, we need to group the numbers from right to left. In the case of 1225, we need to group it as 12 and 25.

Step 2: Now we need to find n whose square is less than or equal to 12. We can say n is ‘3’ because 3 x 3 = 9 is less than 12. Now the quotient is 3, and after subtracting 9 from 12, the remainder is 3.

Step 3: Now let us bring down 25, which is the new dividend. Add the old divisor with the same number, 3 + 3 = 6, which will be our new divisor.

Step 4: The next step is finding 6n x n ≤ 325. Let us consider n as 5; now 65 x 5 = 325.

Step 5: Subtract 325 from 325, and the remainder is 0. The quotient is 35.

Step 6: Since the remainder is 0, we can conclude that √1225 = 35.

Square Root of 1225 by Approximation Method

The approximation method is not necessary for 1225 as it is a perfect square, but it can be used to verify the calculation.

Step 1: We find the closest perfect square to 1225, which are 1225 itself or nearby perfect squares.

Step 2: Since 1225 is a perfect square, √1225 directly gives us an integer value, which is 35.

Common Mistakes and How to Avoid Them in the Square Root of 1225

Students make mistakes while finding square roots, such as forgetting about the negative square root or skipping prime factorization steps. Let us look at a few common mistakes 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 √1024?

Okay, lets begin

The area of the square is 1024 square units.

Explanation

The area of the square = side^2.

The side length is given as √1024.

Area of the square = side^2 = √1024 x √1024 = 32 × 32 = 1024.

Therefore, the area of the square box is 1024 square units.

Well explained 👍

Problem 2

A square-shaped building measuring 1225 square feet is built; if each of the sides is √1225, what will be the square feet of half of the building?

Okay, lets begin

612.5 square feet

Explanation

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

Dividing 1225 by 2 = we get 612.5.

So half of the building measures 612.5 square feet.

Well explained 👍

Problem 3

Calculate √1225 x 4.

Okay, lets begin

140

Explanation

The first step is to find the square root of 1225, which is 35.

The second step is to multiply 35 by 4.

So 35 x 4 = 140.

Well explained 👍

Problem 4

What will be the square root of (625 + 600)?

Okay, lets begin

The square root is 35.

Explanation

To find the square root, we need to find the sum of (625 + 600).

625 + 600 = 1225, and then √1225 = 35.

Therefore, the square root of (625 + 600) is ±35.

Well explained 👍

Problem 5

Find the perimeter of the rectangle if its length ‘l’ is √1225 units and the width ‘w’ is 50 units.

Okay, lets begin

The perimeter of the rectangle is 170 units.

Explanation

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

Perimeter = 2 × (√1225 + 50)

= 2 × (35 + 50)

= 2 × 85

= 170 units.

Well explained 👍

FAQ on Square Root of 1225

1.What is √1225 in its simplest form?

The prime factorization of 1225 is 5 x 5 x 7 x 7, so the simplest form of √1225 = √(5 x 5 x 7 x 7) = 35.

2.Mention the factors of 1225.

Factors of 1225 are 1, 5, 7, 25, 35, 49, 175, 245, and 1225.

3.Calculate the square of 35.

We get the square of 35 by multiplying the number by itself, that is 35 x 35 = 1225.

4.Is 1225 a prime number?

1225 is not a prime number, as it has more than two factors.

5.1225 is divisible by?

1225 has several factors; those are 1, 5, 7, 25, 35, 49, 175, 245, and 1225.

Important Glossaries for the Square Root of 1225

  • Square root: A square root is the inverse of a square. Example: 6^2 = 36, and the inverse of the square is the square root, that is √36 = 6.
     
  • 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: 36, 49, 64, etc.
     
  • Prime factorization: Prime factorization is expressing a number as the product of its prime numbers.
     
  • Integer: An integer is a whole number that can be positive, negative, or zero. Examples include -5, -4, 0, 1, 2, etc.

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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.