Square Root of 1444
2026-02-28 12:43 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. Square roots are used in fields such as vehicle design, finance, etc. Here, we will discuss the square root of 1444.

What is the Square Root of 1444?

The square root is the inverse of the square of the number. 1444 is a perfect square. The square root of 1444 is expressed in both radical and exponential forms. In radical form, it is expressed as √1444, whereas (1444)^(1/2) in exponential form. √1444 = 38, 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 1444

The prime factorization method is used for finding the square root of perfect square numbers. Let's learn how to find the square root using the following methods:

  • Prime factorization method
  • Long division method

Square Root of 1444 by Prime Factorization Method

The product of prime factors is the prime factorization of a number. Now let us look at how 1444 is broken down into its prime factors.

Step 1: Finding the prime factors of 1444 Breaking it down, we get 2 x 2 x 19 x 19: 2^2 x 19^2

Step 2: Now that we have found the prime factors of 1444, we make pairs of those prime factors. Since 1444 is a perfect square, we can pair the factors and take one factor from each pair.

Therefore, the square root of 1444 using prime factorization is 2 x 19 = 38.

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Square Root of 1444 by Long Division Method

The long division method is used for perfect and non-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, we need to group the numbers from right to left. In the case of 1444, we group it as 44 and 14.

Step 2: Now, find n whose square is less than or equal to 14. We can say n is ‘3’ because 3 x 3 = 9, which is less than 14. The quotient is 3 after subtracting 9 from 14, and the remainder is 5.

Step 3: Bring down 44, making the new dividend 544. Add the old divisor with the same number 3, getting 6, which will be part of our new divisor.

Step 4: The new divisor is 6n. We need to find the value of n so that 6n x n ≤ 544. Let's consider n as 8; 68 x 8 = 544.

Step 5: Subtract 544 from 544, getting a remainder of 0, and the quotient is 38.

So the square root of √1444 is 38.

Square Root of 1444 by Approximation Method

Since 1444 is a perfect square, we don't need to use the approximation method to find its square root. However, if needed, we would find it by identifying perfect squares around 1444 and estimating the value, but in this case, we already know that √1444 = 38.

Common Mistakes and How to Avoid Them in the Square Root of 1444

Students may 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 √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 × √1444 = 38 × 38 = 1444.

Therefore, the area of the square box is 1444 square units.

Well explained 👍

Problem 2

A square-shaped building measuring 1444 square feet is built; if each of the sides is √1444, what will be the square feet of half of the building?

Okay, lets begin

722 square feet

Explanation

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

Dividing 1444 by 2 = we get 722.

So half of the building measures 722 square feet.

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Problem 3

Calculate √1444 × 5.

Okay, lets begin

190

Explanation

The first step is to find the square root of 1444, which is 38.

The second step is to multiply 38 by 5.

So 38 × 5 = 190.

Well explained 👍

Problem 4

What will be the square root of (1400 + 44)?

Okay, lets begin

The square root is 38.

Explanation

To find the square root, we need to find the sum of (1400 + 44). 1400 + 44 = 1444, and then √1444 = 38.

Therefore, the square root of (1400 + 44) is ±38.

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Problem 5

Find the perimeter of the rectangle if its length ‘l’ is √1444 units and the width ‘w’ is 50 units.

Okay, lets begin

We find the perimeter of the rectangle as 176 units.

Explanation

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

Perimeter = 2 × (√1444 + 50) = 2 × (38 + 50) = 2 × 88 = 176 units.

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FAQ on Square Root of 1444

1.What is √1444 in its simplest form?

The prime factorization of 1444 is 2 × 2 × 19 × 19, so the simplest form of √1444 = √(2^2 × 19^2) = 2 × 19 = 38.

2.Mention the factors of 1444.

Factors of 1444 are 1, 2, 4, 19, 38, 76, 361, 722, and 1444.

3.Calculate the square of 1444.

We get the square of 1444 by multiplying the number by itself, that is 1444 × 1444 = 2085136.

4.Is 1444 a prime number?

1444 is not a prime number, as it has more than two factors.

5.1444 is divisible by?

1444 has several factors; those are 1, 2, 4, 19, 38, 76, 361, 722, and 1444.

Important Glossaries for the Square Root of 1444

  • 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, which is √16 = 4.
  • Rational number: A rational number can be expressed as the quotient of two integers, p/q, where q is not equal to zero.
  • Perfect square: A perfect square is an integer that is the square of another integer, such as 1444, which is 38^2.
  • Long division method: A technique used to find the square root of a number by dividing and averaging, even for non-perfect squares.
  • Prime factorization: The process of expressing a number as the product of its prime factors.

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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.