Square Root of 4680
2026-02-28 11:41 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-4680

224 Learners

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 various fields such as vehicle design, finance, etc. Here, we will discuss the square root of 4680.

What is the Square Root of 4680?

The square root is the inverse of the square of a number. 4680 is not a perfect square. The square root of 4680 is expressed in both radical and exponential form. In the radical form, it is expressed as √4680, whereas in the exponential form it is expressed as (4680)^(1/2). √4680 ≈ 68.426, 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 4680

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

  • Prime factorization method 
  • Long division method 
  • Approximation method

Square Root of 4680 by Prime Factorization Method

The product of prime factors is the prime factorization of a number. Now let's look at how 4680 is broken down into its prime factors.

Step 1: Finding the prime factors of 4680

Breaking it down, we get 2 x 2 x 2 x 3 x 3 x 5 x 13: 2^3 x 3^2 x 5 x 13

Step 2: We found the prime factors of 4680. The second step is to make pairs of those prime factors. Since 4680 is not a perfect square, the digits of the number can’t be grouped into pairs completely. Therefore, calculating 4680 using prime factorization is not straightforward.

Explore Our Programs

Square Root of 4680 by Long Division Method

The long division method is particularly used for non-perfect square numbers. In this method, we 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: We need to group the numbers from right to left. In the case of 4680, we group it as 80 and 46.

Step 2: Now we need to find n whose square is less than or equal to 46. The closest perfect square is 6 x 6 = 36. So the quotient is 6, after subtracting 36 from 46 the remainder is 10.

Step 3: Bring down 80, making the new dividend 1080. Add the old divisor with the same number 6 + 6 = 12, which will be our new divisor.

Step 4: We need to find the largest digit n such that 12n x n ≤ 1080. Trying n = 8, we get 128 x 8 = 1024.

Step 5: Subtract 1024 from 1080, the remainder is 56. The quotient is 68.

Step 6: Since the dividend is less than the divisor, add a decimal point and bring down two zeroes, making it 5600.

Step 7: Now find the new divisor which is 136 (68 x 2) and find n such that 136n x n ≤ 5600. Trying n = 4, we get 1364 x 4 = 5456.

Step 8: Subtract 5456 from 5600, getting a remainder of 144. Step 9: The quotient is now 68.4 Step 10: Continue these steps until you get the desired precision.

So the square root of √4680 is approximately 68.426.

Square Root of 4680 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 4680 using the approximation method.

Step 1: We need to find two perfect squares between which √4680 falls. The squares of 68 (4624) and 69 (4761) are the closest perfect squares.

Step 2: Use the formula: (Given number - smaller perfect square) / (larger perfect square - smaller perfect square). Applying the formula: (4680 - 4624) ÷ (4761 - 4624) = 56 ÷ 137 ≈ 0.409 Adding this value to the smaller integer value: 68 + 0.409 ≈ 68.409 Thus, √4680 ≈ 68.409.

Common Mistakes and How to Avoid Them in the Square Root of 4680

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.

Download Worksheets

Problem 1

Can you help Max find the area of a square box if its side length is given as √4680?

Okay, lets begin

The area of the square is 4680 square units.

Explanation

The area of the square = side².

The side length is given as √4680.

Area of the square = side² = √4680 x √4680 = 4680.

Therefore, the area of the square box is 4680 square units.

Well explained 👍

Problem 2

A square-shaped park measuring 4680 square feet is built; if each of the sides is √4680, what will be the square feet of half of the park?

Okay, lets begin

2340 square feet.

Explanation

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

Dividing 4680 by 2 = 2340.

So half of the park measures 2340 square feet.

Well explained 👍

Problem 3

Calculate √4680 x 5.

Okay, lets begin

Approximately 342.13.

Explanation

First, find the square root of 4680 which is approximately 68.426, then multiply this by 5.

So 68.426 x 5 ≈ 342.13.

Well explained 👍

Problem 4

What will be the square root of (4680 + 20)?

Okay, lets begin

The square root is approximately 68.593.

Explanation

To find the square root, find the sum of (4680 + 20): 4680 + 20 = 4700.

The square root of 4700 is approximately 68.593.

Well explained 👍

Problem 5

Find the perimeter of the rectangle if its length ‘l’ is √4680 units and the width ‘w’ is 50 units.

Okay, lets begin

The perimeter of the rectangle is approximately 236.852 units.

Explanation

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

Perimeter = 2 × (√4680 + 50) ≈ 2 × (68.426 + 50) ≈ 2 × 118.426 ≈ 236.852 units.

Well explained 👍

FAQ on Square Root of 4680

1.What is √4680 in its simplest form?

The prime factorization of 4680 is 2 x 2 x 2 x 3 x 3 x 5 x 13. The simplest form of √4680 is √(2^3 x 3^2 x 5 x 13).

2.Mention the factors of 4680.

Factors of 4680 include 1, 2, 3, 4, 5, 6, 10, 12, 13, 15, 20, 26, 30, 39, 52, 60, 65, 78, 120, 130, 156, 195, 260, 390, 780, 1170, 1560, 2340, and 4680.

3.Calculate the square of 4680.

The square of 4680 is found by multiplying the number by itself: 4680 x 4680 = 21,902,400.

4.Is 4680 a prime number?

4680 is not a prime number, as it has more than two factors.

5.4680 is divisible by?

4680 is divisible by several numbers, such as 1, 2, 3, 4, 5, 6, 10, 12, 13, 15, 20, 26, 30, 39, 52, 60, 65, 78, 120, 130, 156, 195, 260, 390, 780, 1170, 1560, 2340, and 4680.

Important Glossaries for the Square Root of 4680

  • Square root: A square root is a value that, when multiplied by itself, gives the original number. Example: √16 = 4, because 4 x 4 = 16.
  • Irrational number: An irrational number cannot be written as a simple fraction; it has a non-repeating, non-terminating decimal expansion. Example: √4680 is irrational.
  • Approximation: Estimating a number close to its actual value, often used for irrational numbers.
  • Perfect square: A number that is the square of an integer. Example: 16 is a perfect square because it is 4 squared.
  • Long division method: A technique used to find the square root of a number by dividing it into pairs and finding the closest perfect squares.

What Is Algebra? 🧮 | Simple Explanation with 🎯 Cool Examples for Kids | ✨BrightCHAMPS Math

▶

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.