Square Root of 3720
2026-02-28 17:55 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 the square is a square root. The square root is used in various fields such as vehicle design and finance. Here, we will discuss the square root of 3720.

What is the Square Root of 3720?

The square root is the inverse of the square of the number. 3720 is not a perfect square. The square root of 3720 can be expressed in both radical and exponential forms. In the radical form, it is expressed as √3720, whereas in the exponential form, it is written as (3720)^(1/2). √3720 ≈ 60.9918, 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 3720

The prime factorization method is used for perfect square numbers. For non-perfect square numbers, methods such as the long-division and approximation methods are used. Let us now learn the following methods:

  • Prime factorization method
  • Long division method
  • Approximation method

Square Root of 3720 by Prime Factorization Method

The product of prime factors is the prime factorization of a number. Now let us look at how 3720 is broken down into its prime factors.

Step 1: Finding the prime factors of 3720 Breaking it down, we get 2 x 2 x 2 x 3 x 5 x 31: 2^3 x 3^1 x 5^1 x 31^1

Step 2: Now we have found the prime factors of 3720. Since 3720 is not a perfect square, the digits of the number can’t be grouped into pairs, and thus, calculating the square root of 3720 using prime factorization is not straightforward.

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Square Root of 3720 by Long Division Method

The long division method is particularly useful for non-perfect square numbers. In this method, we should find 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: Begin by pairing numbers from right to left. In the case of 3720, group it as 20 and 37.

Step 2: Find n whose square is less than or equal to 37. We can take n as 6 because 6 x 6 = 36. Now the quotient is 6, and after subtracting 36 from 37, the remainder is 1.

Step 3: Bring down the next pair of digits, 20, making the new dividend 120.

Step 4: Double the current quotient (6), which gives us 12, and set this as the new divisor.

Step 5: Find the largest digit, n, such that 12n x n ≤ 120.

Step 6: Subtract the result from the dividend, adjust the quotient, and continue the process, adding decimal points as necessary to achieve the desired precision.

Square Root of 3720 by Approximation Method

The approximation method is another way to find square roots. It is an easy method for estimating the square root of a given number. Let us learn how to find the square root of 3720 using the approximation method.

Step 1: Identify the closest perfect squares to √3720. The smallest perfect square less than 3720 is 3600 (60^2), and the largest perfect square greater than 3720 is 3721 (61^2). Thus, √3720 falls between 60 and 61.

Step 2: Use linear interpolation to estimate the square root: (3720 - 3600) / (3721 - 3600) = 120 / 121 ≈ 0.9918 Using this approximation, the square root of 3720 is approximately 60.9918.

Common Mistakes and How to Avoid Them in the Square Root of 3720

Students often make mistakes while finding square roots, such as forgetting about the negative square root or skipping steps in the long division method. Let us look at 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 √3380?

Okay, lets begin

The area of the square is approximately 3380 square units.

Explanation

The area of the square = side^2.

The side length is given as √3380.

Area of the square = (√3380) x (√3380) = 58.11 x 58.11 ≈ 3380

Therefore, the area of the square box is approximately 3380 square units.

Well explained 👍

Problem 2

A square-shaped building measuring 3720 square feet is built; if each of the sides is √3720, what will be the square feet of half of the building?

Okay, lets begin

1860 square feet

Explanation

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

Dividing 3720 by 2 = 1860

So, half of the building measures 1860 square feet.

Well explained 👍

Problem 3

Calculate √3720 x 5.

Okay, lets begin

Approximately 304.959

Explanation

First, find the square root of 3720, which is approximately 60.9918.

Then multiply 60.9918 by 5.

So, 60.9918 x 5 ≈ 304.959

Well explained 👍

Problem 4

What will be the square root of (3380 + 40)?

Okay, lets begin

The square root is approximately 58.5235

Explanation

First, find the sum of (3380 + 40) = 3420.

Then take the square root of 3420.

√3420 ≈ 58.5235.

Well explained 👍

Problem 5

Find the perimeter of the rectangle if its length ‘l’ is √3380 units and the width ‘w’ is 38 units.

Okay, lets begin

The perimeter of the rectangle is approximately 212.22 units.

Explanation

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

Perimeter = 2 × (√3380 + 38)

≈ 2 × (58.11 + 38)

≈ 2 × 96.11

≈ 192.22 units.

Well explained 👍

FAQ on Square Root of 3720

1.What is √3720 in its simplest form?

The prime factorization of 3720 is 2^3 x 3^1 x 5^1 x 31^1. The simplest form of √3720 is √(2^3 x 3 x 5 x 31).

2.Mention the factors of 3720.

Factors of 3720 include 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 31, 40, 60, 62, 93, 124, 155, 186, 248, 310, 372, 465, 620, 930, 1240, 1860, and 3720.

3.Calculate the square of 3720.

We get the square of 3720 by multiplying the number by itself: 3720 x 3720 = 13,838,400.

4.Is 3720 a prime number?

5.3720 is divisible by?

3720 has many factors, including 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 31, 40, 60, 62, 93, 124, 155, 186, 248, 310, 372, 465, 620, 930, 1240, 1860, and 3720.

Important Glossaries for the Square Root of 3720

  • Square root: A square root is the inverse operation of squaring a number. For example, if 4^2 = 16, then √16 = 4.
     
  • Irrational number: An irrational number cannot be expressed as a simple fraction, meaning it cannot be written in the form of p/q, where p and q are integers and q is not zero.
     
  • Perfect square: A perfect square is a number that can be expressed as the product of an integer with itself. For example, 36 is a perfect square because 6 x 6 = 36.
     
  • Prime factorization: The process of expressing a number as a product of its prime factors. For example, the prime factorization of 3720 is 2^3 x 3 x 5 x 31.
     
  • Decimal approximation: The process of estimating a non-perfect square root to a certain number of decimal places for practical use. For example, √3720 ≈ 60.9918.

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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.