Square Root of 4480
2026-02-28 12:53 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 various fields, including vehicle design and finance. Here, we will discuss the square root of 4480.

What is the Square Root of 4480?

The square root is the inverse of the square of the number. 4480 is not a perfect square. The square root of 4480 is expressed in both radical and exponential form. In the radical form, it is expressed as √4480, whereas (4480)^(1/2) in the exponential form. √4480 ≈ 66.976, 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 4480

The prime factorization method is typically used for perfect square numbers. However, for non-perfect square numbers like 4480, methods such as long division and approximation are more suitable. Let us now learn the following methods: 

  • Prime factorization method
  • Long division method
  • Approximation method

Square Root of 4480 by Prime Factorization Method

The product of prime factors is the prime factorization of a number. Now let us look at how 4480 is broken down into its prime factors.

Step 1: Finding the prime factors of 4480 Breaking it down, we get 2 × 2 × 2 × 2 × 2 × 5 × 7 × 7: 2^5 × 5^1 × 7^2

Step 2: Now we found out the prime factors of 4480. The second step is to make pairs of those prime factors. Since 4480 is not a perfect square, the digits of the number can’t be grouped in perfect pairs. Calculating √4480 using prime factorization requires approximation.

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Square Root of 4480 by Long Division Method

The long division method is particularly used for non-perfect square numbers. Let's 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 4480, we need to group it as 44 and 80.

Step 2: Now we need to find n whose square is less than or equal to 44. We use n as '6' because 6 × 6 = 36, which is less than 44. Now the quotient is 6, and after subtracting 36 from 44, the remainder is 8.

Step 3: Now let us bring down 80 to make the new dividend 880. 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 ≤ 880. Let n be 7, then 127 × 7 = 889.

Step 5: Subtract 889 from 880; the difference is -9, and the quotient is 67.

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 900.

Step 7: Now we need to find the new divisor. Try n = 7, so 134 × 7 = 938.

Step 8: Subtracting 938 from 900, we get -38.

Step 9: Continue these steps until you have the desired precision. So the square root of √4480 ≈ 66.976.

Square Root of 4480 by Approximation Method

The approximation method is another way of finding square roots; it is straightforward. Now, let us learn how to find the square root of 4480 using the approximation method.

Step 1: Find the closest perfect squares of √4480. The smallest perfect square less than 4480 is 4225 (65^2), and the largest perfect square more than 4480 is 4624 (68^2). Therefore, √4480 falls between 65 and 68.

Step 2: Use the interpolation formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square) (4480 - 4225) / (4624 - 4225) = 0.639 Using the formula, we identified the decimal value to add to the initial estimate. Adding this gives us 65 + 1.639 = 66.639, so the square root of 4480 is approximately 66.976.

Common Mistakes and How to Avoid Them in the Square Root of 4480

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's 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 √4480?

Okay, lets begin

The area of the square is 4480 square units.

Explanation

The area of the square = side^2.

The side length is given as √4480.

Area of the square = side^2 = √4480 × √4480 = 4480.

Therefore, the area of the square box is 4480 square units.

Well explained 👍

Problem 2

A square-shaped plot measuring 4480 square feet is built; if each of the sides is √4480, what will be the square feet of half of the plot?

Okay, lets begin

2240 square feet

Explanation

We can divide the given area by 2 since the plot is square-shaped.

Dividing 4480 by 2, we get 2240.

So half of the plot measures 2240 square feet.

Well explained 👍

Problem 3

Calculate √4480 × 5.

Okay, lets begin

334.88

Explanation

The first step is to find the square root of 4480, which is approximately 66.976.

The second step is to multiply 66.976 by 5.

So, 66.976 × 5 ≈ 334.88.

Well explained 👍

Problem 4

What will be the square root of (4480 + 16)?

Okay, lets begin

The square root is approximately 67.

Explanation

To find the square root, calculate the sum of (4480 + 16). 4480 + 16 = 4496.

Then, √4496 ≈ 67.

Well explained 👍

Problem 5

Find the perimeter of a rectangle if its length 'l' is √4480 units and the width 'w' is 40 units.

Okay, lets begin

The perimeter of the rectangle is approximately 213.952 units.

Explanation

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

Perimeter = 2 × (√4480 + 40) ≈ 2 × (66.976 + 40) ≈ 2 × 106.976 ≈ 213.952 units.

Well explained 👍

FAQ on Square Root of 4480

1.What is √4480 in its simplest form?

The prime factorization of 4480 is 2 × 2 × 2 × 2 × 2 × 5 × 7 × 7, so the simplest form of √4480 = √(2^5 × 5^1 × 7^2).

2.Mention the factors of 4480.

Factors of 4480 are 1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 28, 32, 35, 40, 56, 70, 80, 112, 140, 160, 224, 280, 560, 896, 1120, 2240, and 4480.

3.Calculate the square of 4480.

We find the square of 4480 by multiplying the number by itself, that is 4480 × 4480 = 20,070,400.

4.Is 4480 a prime number?

4480 is not a prime number, as it has more than two factors.

5.4480 is divisible by?

4480 has many factors, including 1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 28, 32, 35, 40, 56, 70, 80, 112, 140, 160, 224, 280, 560, 896, 1120, 2240, and 4480.

Important Glossaries for the Square Root of 4480

  • Square root: A square root is the inverse operation of squaring a number. For example, 4^2 = 16, and the inverse operation is the square root: √16 = 4.
  • Irrational number: An irrational number cannot be exactly expressed as a simple fraction (p/q), where q is not zero.
  • Prime factorization: Breaking down a composite number into a product of its prime factors.
  • Long division method: A method for finding the square root of non-perfect square numbers using a systematic division process.
  • Decimal approximation: The process of estimating the value of a number to its nearest decimal form.

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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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