Square Root of 4840
2026-02-28 01:03 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 and finance. Here, we will discuss the square root of 4840.

What is the Square Root of 4840?

The square root is the inverse of the square of the number. 4840 is not a perfect square. The square root of 4840 is expressed in both radical and exponential forms. In the radical form, it is expressed as √4840, whereas in the exponential form it is expressed as (4840)^(1/2). √4840 ≈ 69.535, 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 4840

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 4840 by Prime Factorization Method

The product of prime factors is the prime factorization of a number. Now let us look at how 4840 is broken down into its prime factors.

Step 1: Finding the prime factors of 4840

Breaking it down, we get 2 × 2 × 2 × 5 × 11 × 11: 2^3 × 5^1 × 11^2

Step 2: Now we found out the prime factors of 4840. The second step is to make pairs of those prime factors. Since 4840 is not a perfect square, the digits of the number can’t be grouped in pairs perfectly. Therefore, calculating √4840 using prime factorization will only give an approximate value.

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Square Root of 4840 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 4840, we need to group it as 48 and 40.

Step 2: Now we need to find n whose square is less than or equal to 48. We can say n is ‘6’ because 6 × 6 = 36, which is less than or equal to 48. Now the quotient is 6. Subtracting 36 from 48, the remainder is 12.

Step 3: Bring down 40, which is the new dividend. Add the old divisor with the same number: 6 + 6 = 12, which will be our new divisor.

Step 4: The new divisor will be 12n. We need to find the value of n such that 12n × n is less than or equal to 1240. Let us consider n as 9: 129 × 9 = 1161.

Step 5: Subtracting 1161 from 1240 gives a remainder of 79.

Step 6: Since the dividend is less than the new 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 7900.

Step 7: Find the new divisor, which is 138. Continuing this process will yield the square root of 4840 as approximately 69.535.

Square Root of 4840 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 4840 using the approximation method.

Step 1: We need to find the closest perfect squares to 4840. The smallest perfect square less than 4840 is 4761 (69^2), and the largest perfect square greater than 4840 is 4900 (70^2). √4840 falls somewhere between 69 and 70.

Step 2: Apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Going by the formula (4840 - 4761) / (4900 - 4761) ≈ 0.535 Using the formula, we identified the decimal point of our square root. The next step is adding the initial integer value to the decimal number: 69 + 0.535 = 69.535, so the square root of 4840 is approximately 69.535.

Common Mistakes and How to Avoid Them in the Square Root of 4840

Students do make mistakes while finding the square root, such as forgetting about the negative square root or skipping long division methods. Now let us look at a few 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 √4840?

Okay, lets begin

The area of the square is approximately 4840 square units.

Explanation

The area of the square = side^2.

The side length is given as √4840.

Area of the square = side^2 = √4840 × √4840 = 4840.

Therefore, the area of the square box is approximately 4840 square units.

Well explained 👍

Problem 2

A square-shaped building measuring 4840 square feet is built; if each of the sides is √4840, what will be the square feet of half of the building?

Okay, lets begin

2420 square feet

Explanation

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

Dividing 4840 by 2 = we get 2420.

So half of the building measures 2420 square feet.

Well explained 👍

Problem 3

Calculate √4840 × 5.

Okay, lets begin

Approximately 347.675

Explanation

The first step is to find the square root of 4840, which is approximately 69.535.

The second step is to multiply 69.535 by 5.

So 69.535 × 5 ≈ 347.675.

Well explained 👍

Problem 4

What will be the square root of (4840 + 60)?

Okay, lets begin

The square root is approximately 70.5.

Explanation

To find the square root, we need to find the sum of (4840 + 60). 4840 + 60 = 4900, and then √4900 = 70.

Therefore, the square root of (4840 + 60) is ±70.

Well explained 👍

Problem 5

Find the perimeter of the rectangle if its length ‘l’ is √4840 units and the width ‘w’ is 60 units.

Okay, lets begin

The perimeter of the rectangle is approximately 259.07 units.

Explanation

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

Perimeter = 2 × (√4840 + 60) = 2 × (69.535 + 60) ≈ 2 × 129.535 ≈ 259.07 units.

Well explained 👍

FAQ on Square Root of 4840

1.What is √4840 in its simplest form?

The prime factorization of 4840 is 2 × 2 × 2 × 5 × 11 × 11, so the simplest form of √4840 is √(2^3 × 5 × 11^2).

2.Mention the factors of 4840.

Factors of 4840 are 1, 2, 4, 5, 8, 10, 11, 20, 22, 40, 44, 55, 88, 110, 220, 242, 440, 484, 1210, 2420, and 4840.

3.Calculate the square of 4840.

We get the square of 4840 by multiplying the number by itself, that is 4840 × 4840 = 23,425,600.

4.Is 4840 a prime number?

4840 is not a prime number, as it has more than two factors.

5.4840 is divisible by?

4840 has many factors; those are 1, 2, 4, 5, 8, 10, 11, 20, 22, 40, 44, 55, 88, 110, 220, 242, 440, 484, 1210, 2420, and 4840.

Important Glossaries for the Square Root of 4840

  • 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.
  • Principal square root: A number has both positive and negative square roots; however, it is always the positive square root that has more prominence due to its uses in the real world. That is the reason it is also known as a principal square root.
  • Long division method: A technique used to find the square root of a number by dividing and averaging iteratively.
  • 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.

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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.