Square Root of 2520
2026-02-28 00:43 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. The square root is used in the field of vehicle design, finance, etc. Here, we will discuss the square root of 2520.

What is the Square Root of 2520?

The square root is the inverse of the square of the number. 2520 is not a perfect square. The square root of 2520 is expressed in both radical and exponential form. In the radical form, it is expressed as √2520, whereas (2520)^(1/2) in the exponential form. √2520 ≈ 50.199, 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 2520

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 2520 by Prime Factorization Method

The product of prime factors is the prime factorization of a number. Now let us look at how 2520 is broken down into its prime factors:

Step 1: Finding the prime factors of 2520 Breaking it down, we get 2 × 2 × 2 × 3 × 3 × 5 × 7: 2^3 × 3^2 × 5 × 7

Step 2: Now we found out the prime factors of 2520. The second step is to make pairs of those prime factors. Since 2520 is not a perfect square, the digits of the number can’t be grouped in pairs completely.

Therefore, calculating √2520 using prime factorization requires approximations and simplifications.

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Square Root of 2520 by Long Division Method

The long division method is particularly used for non-perfect square numbers. In this method, we 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 2520, we need to group it as 20 and 25.

Step 2: Now we need to find n whose square is less than or equal to 25. We can say n is ‘5’ because 5 × 5 = 25. Now the quotient is 5, and after subtracting 25 - 25, the remainder is 0.

Step 3: Now let us bring down 20, which is the new dividend. Add the old divisor with the same number (5 + 5), we get 10, which will be our new divisor.

Step 4: The new divisor will be the sum of the dividend and quotient. Now we get 10n as the new divisor, we need to find the value of n.

Step 5: The next step is finding 10n × n ≤ 20. Let us consider n as 2, now 10 × 2 × 2 = 40, which is not possible, so we need to find a smaller n.

Step 6: Subtract 20 from 10, the difference is 10, and the quotient is 50.

Step 7: 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 1000.

Step 8: Now we need to find the new divisor that is 1005 because 1005 × 1 = 1005, which is not possible. We need to adjust n and divisor to fit.

Step 9: Subtracting is adjusted to find an appropriate value, resulting in a more precise decimal.

Step 10: Now the quotient is approximately 50.2

Step 11: Continue doing these steps until we get two numbers after the decimal point. Suppose if there are no decimal values continue till the remainder is zero.

So the square root of √2520 is approximately 50.2.

Square Root of 2520 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 2520 using the approximation method.

Step 1: Now we have to find the closest perfect square of √2520. The smallest perfect square less than 2520 is 2500 (since 50^2 = 2500) and the largest perfect square greater than 2520 is 2601 (since 51^2 = 2601). √2520 falls somewhere between 50 and 51.

Step 2: Now we need to apply the formula that is (Given number - smallest perfect square) ÷ (Greater perfect square - smallest perfect square). Going by the formula (2520 - 2500) ÷ (2601 - 2500) = 20 ÷ 101 ≈ 0.198. Using the formula we identified the decimal point of our square root. The next step is adding the value we got initially to the decimal number which is 50 + 0.2 ≈ 50.2.

So the square root of 2520 is approximately 50.2.

Common Mistakes and How to Avoid Them in the Square Root of 2520

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 √2520?

Okay, lets begin

The area of the square is approximately 2520 square units.

Explanation

The area of the square = side^2.

The side length is given as √2520.

Area of the square = side^2

= √2520 × √2520

= 2520.

Therefore, the area of the square box is approximately 2520 square units.

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Problem 2

A square-shaped building measuring 2520 square feet is built; if each of the sides is √2520, what will be the square feet of half of the building?

Okay, lets begin

1260 square feet

Explanation

We can just divide the given area by 2 as the building is square-shaped. Dividing 2520 by 2 = we get 1260. So half of the building measures 1260 square feet.

Well explained 👍

Problem 3

Calculate √2520 × 5.

Okay, lets begin

Approx. 250.995

Explanation

The first step is to find the square root of 2520, which is approximately 50.199, the second step is to multiply 50.199 with 5.

So 50.199 × 5 ≈ 250.995.

Well explained 👍

Problem 4

What will be the square root of (2500 + 20)?

Okay, lets begin

The square root is approximately 50.2

Explanation

To find the square root, we need to find the sum of (2500 + 20).

2500 + 20 = 2520, and then √2520 ≈ 50.2.

Therefore, the square root of (2500 + 20) is approximately ±50.2.

Well explained 👍

Problem 5

Find the perimeter of the rectangle if its length ‘l’ is √2520 units and the width ‘w’ is 20 units.

Okay, lets begin

We find the perimeter of the rectangle as approximately 140.4 units.

Explanation

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

Perimeter = 2 × (√2520 + 20)

= 2 × (50.2 + 20)

= 2 × 70.2

≈ 140.4 units.

Well explained 👍

FAQ on Square Root of 2520

1.What is √2520 in its simplest form?

The prime factorization of 2520 is 2^3 × 3^2 × 5 × 7, so the simplest form of √2520 is √(2^3 × 3^2 × 5 × 7).

2.Mention the factors of 2520.

Factors of 2520 are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 18, 20, 21, 24, 28, 30, 35, 36, 40, 42, 45, 56, 60, 63, 70, 72, 84, 90, 105, 120, 126, 140, 168, 180, 210, 252, 280, 315, 360, 420, 504, 630, 840, 1260, and 2520.

3.Calculate the square of 2520.

We get the square of 2520 by multiplying the number by itself, that is 2520 × 2520 = 6350400.

4.Is 2520 a prime number?

2520 is not a prime number, as it has more than two factors.

5.2520 is divisible by?

2520 has many factors; those are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 18, 20, 21, 24, 28, 30, 35, 36, 40, 42, 45, 56, 60, 63, 70, 72, 84, 90, 105, 120, 126, 140, 168, 180, 210, 252, 280, 315, 360, 420, 504, 630, 840, 1260, and 2520.

Important Glossaries for the Square Root of 2520

  • 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.
     
  • Perfect square: A perfect square is a number that is the square of an integer. Example: 49 is a perfect square because 7 × 7 = 49.
     
  • Decimal: If a number has a whole number and a fraction in a single number then it is called a decimal. For example: 7.86, 8.65, and 9.42 are decimals.
     
  • Prime factorization: Prime factorization is writing a number as a product of its prime factors. Example: 30 can be written as 2 × 3 × 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.

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: He loves to play the quiz with kids through algebra to make kids love it.