Square Root of 1252
2026-02-28 17:15 Diff
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Last updated on August 5, 2025

If a number is multiplied by itself, the result is a square. The inverse of squaring a number is finding its square root. The square root is used in fields such as vehicle design, finance, and more. Here, we will discuss the square root of 1252.

What is the Square Root of 1252?

The square root is the inverse of squaring a number. 1252 is not a perfect square. The square root of 1252 is expressed in both radical and exponential form. In radical form, it is expressed as √1252, whereas in exponential form it is expressed as (1252)^(1/2). √1252 ≈ 35.37983, 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 1252

The prime factorization method is used for perfect square numbers. However, for non-perfect square numbers, the prime factorization method is not suitable, and methods like long division and approximation are used. Let's explore these methods:

  • Prime factorization method
  • Long division method
  • Approximation method

Square Root of 1252 by Prime Factorization Method

The prime factorization of a number is the product of its prime factors. Now, let's look at how 1252 is broken down into its prime factors.

Step 1: Finding the prime factors of 1252 Breaking it down, we get 2 x 2 x 313: 2^2 x 313^1

Step 2: We have found the prime factors of 1252. Since 1252 is not a perfect square, the prime factors cannot be grouped into pairs.

Therefore, calculating √1252 using prime factorization alone is not possible.

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Square Root of 1252 by Long Division Method

The long division method is particularly useful for non-perfect square numbers. In this method, we find the closest perfect square number to the given number. Let's 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. For 1252, group it as 52 and 12.

Step 2: Find n whose square is less than or equal to 12. Here, n is 3 because 3 x 3 = 9, which is less than 12. The quotient is 3, and the remainder is 12 - 9 = 3.

Step 3: Bring down 52, making the new dividend 352. Add the old divisor (3) to itself to form the new divisor, 6.

Step 4: Find n such that 6n x n is less than or equal to 352. Let n = 5. Then, 65 x 5 = 325.

Step 5: Subtract 325 from 352, giving a remainder of 27. The quotient becomes 35.

Step 6: Since the dividend is less than the divisor, add a decimal point and bring down 00, making the new dividend 2700.

Step 7: Find n such that 700n x n is less than or equal to 2700. Let n = 3. Then, 703 x 3 = 2109.

Step 8: Subtract 2109 from 2700, giving a remainder of 591.

Step 9: Continue this process until you achieve the desired precision.

The square root of √1252 is approximately 35.38.

Square Root of 1252 by Approximation Method

The approximation method is another way to find square roots quickly. Let's find the square root of 1252 using this method.

Step 1: Identify the closest perfect squares around 1252. The smallest perfect square less than 1252 is 1225, and the largest is 1296. Thus, √1252 falls between 35 and 36.

Step 2: Use interpolation to approximate: (1252 - 1225) / (1296 - 1225) = 27 / 71 ≈ 0.38. Adding this decimal to the lower integer gives 35 + 0.38 = 35.38, so the square root of 1252 is approximately 35.38.

Common Mistakes and How to Avoid Them in the Square Root of 1252

Students often make mistakes when finding square roots, such as forgetting about the negative square root or skipping steps in the long division method. Let's examine 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 √1252?

Okay, lets begin

The area of the square is approximately 1252 square units.

Explanation

The area of a square is calculated as side^2.

The side length is given as √1252.

Area = (√1252) x (√1252) = 1252.

Therefore, the area of the square box is approximately 1252 square units.

Well explained 👍

Problem 2

A square-shaped building measuring 1252 square feet is built; if each of the sides is √1252, what will be the square feet of half of the building?

Okay, lets begin

626 square feet

Explanation

To find half of the building's area, simply divide the total area by 2.

Dividing 1252 by 2 gives 626.

So half of the building measures 626 square feet.

Well explained 👍

Problem 3

Calculate √1252 x 5.

Okay, lets begin

Approximately 176.89915

Explanation

First, find the square root of 1252, which is approximately 35.37983.

Then multiply by 5.

35.37983 x 5 = 176.89915.

Well explained 👍

Problem 4

What will be the square root of (1252 + 48)?

Okay, lets begin

The square root is 36.

Explanation

First, find the sum of 1252 and 48, which is 1300.

The closest perfect square to 1300 is 1296, and √1296 is 36.

Therefore, the square root of (1252 + 48) is approximately 36.

Well explained 👍

Problem 5

Find the perimeter of the rectangle if its length ‘l’ is √1252 units and the width ‘w’ is 38 units.

Okay, lets begin

The perimeter of the rectangle is approximately 146.76 units.

Explanation

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

Perimeter = 2 × (√1252 + 38)

= 2 × (35.37983 + 38)

≈ 2 × 73.37983

= 146.76 units.

Well explained 👍

FAQ on Square Root of 1252

1.What is √1252 in its simplest form?

The prime factorization of 1252 is 2 x 2 x 313, so the simplest form of √1252 is √(2 x 2 x 313).

2.Mention the factors of 1252.

Factors of 1252 are 1, 2, 4, 313, 626, and 1252.

3.Calculate the square of 1252.

The square of 1252 is 1252 x 1252 = 1,567,504.

4.Is 1252 a prime number?

1252 is not a prime number, as it has more than two factors.

5.1252 is divisible by?

1252 is divisible by 1, 2, 4, 313, 626, and 1252.

Important Glossaries for the Square Root of 1252

  • Square root: A square root is the inverse operation of squaring a number. For example, 4^2 = 16, and the inverse is the square root, √16 = 4.
     
  • Irrational number: An irrational number cannot be expressed as a simple fraction. It has a non-repeating, non-terminating decimal expansion.
     
  • Long division method: A step-by-step approach to finding square roots, especially for non-perfect squares, involving division and approximation.
     
  • Approximation method: A method used to find a close estimate of the square root of a number by identifying nearby perfect squares and interpolating between them.
     
  • Interpolation: A mathematical method used to estimate values between two known values, often used in approximation methods for finding square roots.

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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.