Square Root of 1744
2026-02-28 13:33 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 fields such as vehicle design, finance, etc. Here, we will discuss the square root of 1744.

What is the Square Root of 1744?

The square root is the inverse of the square of the number. 1744 is not a perfect square. The square root of 1744 is expressed in both radical and exponential form. In the radical form, it is expressed as √1744, whereas (1744)^(1/2) in the exponential form. √1744 ≈ 41.758, 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 1744

The prime factorization method is used for perfect square numbers. However, the prime factorization method is not used for non-perfect square numbers where the 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 1744 by Prime Factorization Method

The product of prime factors is the prime factorization of a number. Now let us look at how 1744 is broken down into its prime factors.

Step 1: Finding the prime factors of 1744 Breaking it down, we get 2 x 2 x 2 x 2 x 109: 2^4 x 109^1

Step 2: Now we have found the prime factors of 1744. The second step is to make pairs of those prime factors. Since 1744 is not a perfect square, the digits of the number can’t be grouped in pairs to form a perfect square.

Therefore, calculating √1744 using prime factorization requires approximation.

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Square Root of 1744 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: To begin with, we need to group the numbers from right to left. In the case of 1744, we need to group it as 44 and 17.

Step 2: Now we need to find n whose square is ≤ 17. We can say n is ‘4’ because 4 x 4 = 16 is less than or equal to 17. Now the quotient is 4, and after subtracting 16 from 17, the remainder is 1.

Step 3: Now let us bring down 44, which is the new dividend. Add the old divisor with the same number 4 + 4 = 8, which will be our new divisor.

Step 4: The new divisor will be 8n, and we need to find the value of n such that 8n x n ≤ 144. Let us consider n as 1, now 81 x 1 = 81.

Step 5: Subtract 81 from 144, the difference is 63, and the quotient is 41.

Step 6: Since the dividend is less than the divisor, we need to add a decimal point. Adding the decimal point allows us to add two zeros to the dividend. Now the new dividend is 6300.

Step 7: Now we need to find the new divisor, which is 418 because 418 x 8 = 3344.

Step 8: Subtracting 3344 from 6300, we get the result 2956.

Step 9: Continue doing these steps until we get the desired number of decimal places.

So the square root of √1744 is approximately 41.758.

Square Root of 1744 by Approximation Method

The approximation method is another method for finding 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 1744 using the approximation method.

Step 1: Now we have to find the closest perfect square to √1744.

The smallest perfect square less than 1744 is 1600, and the largest perfect square greater than 1744 is 1764.

√1744 falls somewhere between 40 and 42.

Step 2: Now we need to apply the formula:

(Given number - smallest perfect square) / (Greater perfect square - smallest perfect square).

Going by the formula: (1744 - 1600) / (1764 - 1600) = 144 / 164 ≈ 0.878.

Using the formula, we identified the decimal point of our square root.

The next step is adding the integer part, which is 40, to the decimal number we found: 40 + 0.878 = 40.878.

Thus, the approximate square root of 1744 is 40.878.

Common Mistakes and How to Avoid Them in the Square Root of 1744

Students do make mistakes while finding the square root, such as 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 √1444?

Okay, lets begin

The area of the square is 1444 square units.

Explanation

The area of the square = side^2. The side length is given as √1444. Area of the square = side^2 = √1444 x √1444 = 38 x 38 = 1444. Therefore, the area of the square box is 1444 square units.

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Problem 2

A square-shaped building measuring 1744 square feet is built; if each of the sides is √1744, what will be the square feet of half of the building?

Okay, lets begin

872 square feet

Explanation

We can just divide the given area by 2 as the building is square-shaped. Dividing 1744 by 2 = we get 872. So half of the building measures 872 square feet.

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Problem 3

Calculate √1744 x 5.

Okay, lets begin

208.79

Explanation

The first step is to find the square root of 1744, which is approximately 41.758. The second step is to multiply 41.758 by 5. So 41.758 x 5 ≈ 208.79.

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Problem 4

What will be the square root of (1444 + 300)?

Okay, lets begin

The square root is approximately 42.66.

Explanation

To find the square root, we need to find the sum of (1444 + 300). 1444 + 300 = 1744, and then √1744 ≈ 41.758. Therefore, the square root of (1444 + 300) is approximately 41.758.

Well explained 👍

Problem 5

Find the perimeter of the rectangle if its length ‘l’ is √1444 units and the width ‘w’ is 38 units.

Okay, lets begin

We find the perimeter of the rectangle as 152 units.

Explanation

Perimeter of the rectangle = 2 × (length + width). Perimeter = 2 × (√1444 + 38) = 2 × (38 + 38) = 2 × 76 = 152 units.

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FAQ on Square Root of 1744

1.What is √1744 in its simplest form?

The prime factorization of 1744 is 2 x 2 x 2 x 2 x 109, so the simplest form of √1744 is √(2^4 x 109).

2.Mention the factors of 1744.

Factors of 1744 are 1, 2, 4, 8, 16, 109, 218, 436, 872, and 1744.

3.Calculate the square of 1744.

We get the square of 1744 by multiplying the number by itself, that is 1744 x 1744 = 3,042,816.

4.Is 1744 a prime number?

1744 is not a prime number, as it has more than two factors.

5.1744 is divisible by?

1744 has several factors; those are 1, 2, 4, 8, 16, 109, 218, 436, 872, and 1744.

Important Glossaries for the Square Root of 1744

  • 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.
     
  • Irrational number: An irrational number is a number that cannot be written in the form of p/q, where q is not equal to zero and p and q are integers.
     
  • Prime factorization: Breaking down a number into its basic prime number factors.
     
  • Long division method: A step-by-step process of dividing a number to find its square root, especially useful for non-perfect squares.
     
  • Approximation method: A method used to estimate the square root of a number by comparing it to the nearest perfect squares.

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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.

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