Square Root of 1372
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 the field of vehicle design, finance, etc. Here, we will discuss the square root of 1372.

What is the Square Root of 1372?

The square root is the inverse of the square of the number. 1372 is not a perfect square. The square root of 1372 is expressed in both radical and exponential form. In the radical form, it is expressed as √1372, whereas (1372)^(1/2) in the exponential form. √1372 ≈ 37.041, 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 1372

The prime factorization method is used for perfect square numbers. However, for non-perfect square numbers, 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 1372 by Prime Factorization Method

The product of prime factors is the prime factorization of a number. Now let us look at how 1372 is broken down into its prime factors.

Step 1: Finding the prime factors of 1372.

Breaking it down, we get 2 x 2 x 343: 2^2 x 7^3.

Step 2: Now we have found the prime factors of 1372. The second step is to make pairs of those prime factors. Since 1372 is not a perfect square, the digits of the number can’t be grouped in pairs. Therefore, calculating 1372 using prime factorization is not straightforward.

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Square Root of 1372 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 1372, we can group it as 13 and 72.

Step 2: Now we need to find n whose square is less than or equal to 13. We can say n is 3 because 3 x 3 = 9 is lesser than 13. Now the quotient is 3 after subtracting 13 - 9, and the remainder is 4.

Step 3: Now let us bring down 72, making the new dividend 472. Add the old divisor with the same number, 3 + 3, we get 6, which will be our new divisor.

Step 4: We need to find a number such that 6n x n ≤ 472. Let us consider n as 7, as 67 x 7 = 469.

Step 5: Subtract 469 from 472, and the difference is 3.

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 zeroes to the dividend. Now the new dividend is 300.

Step 7: The new divisor is 74, because 740 x 4 = 296.

Step 8: Subtracting 296 from 300, we get the remainder 4.

Step 9: Continue doing these steps until we get two numbers after the decimal point.

The quotient is approximately 37.04.

Square Root of 1372 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. Let us learn how to find the square root of 1372 using the approximation method.

Step 1: Now we have to find the closest perfect squares to √1372. The smallest perfect square less than 1372 is 1369, and the largest perfect square greater than 1372 is 1444. √1372 falls somewhere between 37 and 38.

Step 2: Apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Using the formula (1372 - 1369) / (1444 - 1369) = 3 / 75 = 0.04. The square root of 1372 is approximately 37 + 0.04 = 37.04.

Common Mistakes and How to Avoid Them in the Square Root of 1372

Students do make mistakes while finding the square root, such as forgetting about the negative square root or skipping long division methods. Let us look at a few of those 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 √138?

Okay, lets begin

The area of the square is 138 square units.

Explanation

The area of the square = side^2.

The side length is given as √138.

Area of the square = side^2 = √138 x √138 = 138.

Therefore, the area of the square box is 138 square units.

Well explained 👍

Problem 2

A square-shaped building measuring 1372 square feet is built; if each of the sides is √1372, what will be the square feet of half of the building?

Okay, lets begin

686 square feet.

Explanation

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

Dividing 1372 by 2 = we get 686.

So half of the building measures 686 square feet.

Well explained 👍

Problem 3

Calculate √1372 x 5.

Okay, lets begin

185.205

Explanation

The first step is to find the square root of 1372, which is approximately 37.041.

The second step is to multiply 37.041 by 5.

So, 37.041 x 5 = 185.205.

Well explained 👍

Problem 4

What will be the square root of (1369 + 3)?

Okay, lets begin

The square root is approximately 37.04.

Explanation

To find the square root, we need to find the sum of (1369 + 3). 1369 + 3 = 1372, and then √1372 ≈ 37.04. Therefore, the square root of (1369 + 3) is approximately 37.04.

Well explained 👍

Problem 5

Find the perimeter of the rectangle if its length ‘l’ is √1372 units and the width ‘w’ is 38 units.

Okay, lets begin

We find the perimeter of the rectangle as approximately 150.082 units.

Explanation

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

Perimeter = 2 × (√1372 + 38) ≈ 2 × (37.041 + 38) ≈ 2 × 75.041 = 150.082 units.

Well explained 👍

FAQ on Square Root of 1372

1.What is √1372 in its simplest form?

The prime factorization of 1372 is 2 x 2 x 7 x 7 x 7, so the simplest form of √1372 = √(2^2 x 7^3).

2.Mention the factors of 1372.

Factors of 1372 are 1, 2, 4, 7, 14, 28, 49, 98, 196, 343, 686, and 1372.

3.Calculate the square of 1372.

We get the square of 1372 by multiplying the number by itself, that is 1372 x 1372 = 1,882,384.

4.Is 1372 a prime number?

1372 is not a prime number, as it has more than two factors.

5.1372 is divisible by?

1372 has several factors; those are 1, 2, 4, 7, 14, 28, 49, 98, 196, 343, 686, and 1372.

Important Glossaries for the Square Root of 1372

  • Square root: The square root of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 16 is 4, since 4 x 4 = 16.
  • Irrational number: An irrational number is a number that cannot be written as a simple fraction - that is, it cannot be expressed as a ratio of two integers.
  • Principal square root: A number has both positive and negative square roots. The principal square root is the non-negative square root of a number.
  • Prime factorization: Breaking down a composite number into its prime factors. For example, the prime factorization of 1372 is 2 x 2 x 7 x 7 x 7.
  • Decimal: A decimal is a number that consists of a whole number and a fractional part separated by a decimal point. For example, 37.041 is a decimal number.

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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.