Square Root of 1348
2026-02-28 08:45 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 1348.

What is the Square Root of 1348?

The square root is the inverse operation of squaring a number. 1348 is not a perfect square. The square root of 1348 is expressed in both radical and exponential form. In the radical form, it is expressed as √1348, whereas (1348)^(1/2) in the exponential form. √1348 ≈ 36.719, 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 1348

The prime factorization method is used for perfect square numbers. However, the prime factorization method is not used for non-perfect square numbers where 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 1348 by Prime Factorization Method

The prime factorization of a number is its expression as a product of prime factors. Now let us look at how 1348 is broken down into its prime factors:

Step 1: Finding the prime factors of 1348

Breaking it down, we get 2 x 2 x 337: 2^2 x 337^1

Step 2: Now that we have found the prime factors of 1348, we attempt to make pairs of those prime factors. Since 1348 is not a perfect square, calculating √1348 using prime factorization is not straightforward.

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Square Root of 1348 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: Start by grouping the digits of 1348 from right to left in pairs. We have 13 and 48.

Step 2: Find the largest number whose square is less than or equal to 13. This number is 3, since 3 x 3 = 9.

Step 3: Subtract 9 from 13 to get 4. Bring down the next pair, 48, to have 448.

Step 4: Double the divisor (3) to get 6, and set up a new divisor as 6n, where n is a digit that, when placed next to 6, forms a number that fits into 448.

Step 5: Determine n such that 6n x n is less than or equal to 448. Let n be 7, as 67 x 7 = 469 is too large, and 66 x 6 = 396 fits.

Step 6: Subtract 396 from 448 to get 52.

Step 7: Bring down two zeros to make it 5200, and repeat the process to get more decimal places.

Step 8: Continue the process to get a more precise value, yielding approximately √1348 ≈ 36.719.

Square Root of 1348 by Approximation Method

The approximation method is another method for finding the square roots; it is an easy method to find the square root of a given number. Now let us learn how to find the square root of 1348 using the approximation method:

Step 1: Identify the closest perfect squares around 1348. The smallest perfect square less than 1348 is 1296 (36^2) and the largest perfect square greater than 1348 is 1369 (37^2).

Step 2: Since √1348 is between 36 and 37, we can use the formula: (Given number - smaller perfect square) / (larger perfect square - smaller perfect square)

Step 3: Apply the formula: (1348 - 1296) / (1369 - 1296) = 52 / 73 ≈ 0.712 Step 4: Add this decimal to the smaller square root: 36 + 0.712 = 36.712. So √1348 ≈ 36.719.

Common Mistakes and How to Avoid Them in the Square Root of 1348

Students do make mistakes while finding the square root, such as forgetting about the negative square root or skipping steps in the long division method. Let us look at a few of these 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 √1348?

Okay, lets begin

The area of the square is 1348 square units.

Explanation

The area of the square = side^2.

The side length is given as √1348.

Area of the square = side^2 = √1348 x √1348 = 1348.

Therefore, the area of the square box is 1348 square units.

Well explained 👍

Problem 2

A square-shaped piece of land measuring 1348 square feet is being developed; if each of the sides is √1348, what will be the square feet of half of the land?

Okay, lets begin

674 square feet

Explanation

We can simply divide the given area by 2 since the land is square-shaped.

Dividing 1348 by 2 gives us 674.

So half of the land measures 674 square feet.

Well explained 👍

Problem 3

Calculate √1348 x 5.

Okay, lets begin

183.595

Explanation

The first step is to find the square root of 1348, which is approximately 36.719.

The second step is to multiply 36.719 by 5.

So 36.719 x 5 = 183.595.

Well explained 👍

Problem 4

What will be the square root of (1348 + 21)?

Okay, lets begin

The square root is approximately 37.

Explanation

To find the square root, first find the sum of (1348 + 21). 1348 + 21 = 1369, and √1369 = 37.

Therefore, the square root of (1348 + 21) is ±37.

Well explained 👍

Problem 5

Find the perimeter of the rectangle if its length ‘l’ is √1348 units and the width ‘w’ is 40 units.

Okay, lets begin

The perimeter of the rectangle is approximately 153.438 units.

Explanation

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

Perimeter = 2 × (√1348 + 40) = 2 × (36.719 + 40) = 2 × 76.719 = 153.438 units.

Well explained 👍

FAQ on Square Root of 1348

1.What is √1348 in its simplest form?

The prime factorization of 1348 is 2 x 2 x 337, so the simplest form of √1348 is √(2^2 x 337).

2.Mention the factors of 1348.

Factors of 1348 are 1, 2, 4, 337, 674, and 1348.

3.Calculate the square of 1348.

We get the square of 1348 by multiplying the number by itself, which is 1348 x 1348 = 1,818,304.

4.Is 1348 a prime number?

1348 is not a prime number, as it has more than two factors.

5.1348 is divisible by?

1348 has several factors; those are 1, 2, 4, 337, 674, and 1348.

Important Glossaries for the Square Root of 1348

  • Square root: A square root of a number is a value that, when multiplied by itself, gives the original number. Example: 4^2 = 16, and the square root of 16 is √16 = 4.
  • Irrational number: An irrational number is a number that cannot be written as a simple fraction - it has a non-repeating, non-terminating decimal expansion.
  • Perfect square: A perfect square is an integer that is the square of another integer. For example, 36 is a perfect square because it is 6^2.
  • Long division method: A technique used to find the square root of a number by dividing and averaging, typically used for non-perfect squares.
  • Radical notation: The expression of a square root using the radical sign (√). For example, √25 = 5.

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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.