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Last updated on May 26th, 2025

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Square Root of 3360

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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 fields such as vehicle design, finance, etc. Here, we will discuss the square root of 3360.

Square Root of 3360 for Omani Students
Professor Greenline from BrightChamps

What is the Square Root of 3360?

The square root is the inverse of the square of a number. 3360 is not a perfect square. The square root of 3360 is expressed in both radical and exponential form. In radical form, it is expressed as √3360, whereas in exponential form it is expressed as (3360)^(1/2). √3360 ≈ 57.9332, 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.

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Finding the Square Root of 3360

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
Professor Greenline from BrightChamps

Square Root of 3360 by Prime Factorization Method

The product of prime factors is the prime factorization of a number. Now let us look at how 3360 is broken down into its prime factors.

 

Step 1: Finding the prime factors of 3360 Breaking it down, we get 2 x 2 x 2 x 2 x 3 x 5 x 7 x 7: 2^4 x 3 x 5 x 7^2

 

Step 2: Now we found the prime factors of 3360. The next step is to make pairs of those prime factors. Since 3360 is not a perfect square, the digits of the number can’t be grouped into pairs completely. Therefore, calculating √3360 using prime factorization directly is not feasible.

Professor Greenline from BrightChamps

Square Root of 3360 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, group the numbers from right to left. In the case of 3360, we need to group it as 33 and 60.

 

Step 2: Now find n whose square is less than or equal to 33. We can say n is '5' because 5 x 5 = 25, which is less than 33. The quotient is 5 after subtracting 25 from 33, the remainder is 8.

 

Step 3: Bring down 60, making the new dividend 860. Add the old divisor with the same number: 5 + 5 = 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 ≤ 860. Let us consider n as 8, now 108 x 8 = 864, which is greater than 860. Trying n as 7, we have 107 x 7 = 749.

 

Step 6: Subtract 749 from 860, the difference is 111, and the quotient is 57.

 

Step 7: Since the dividend is less than the divisor, add a decimal point. Adding the decimal point allows us to add two zeroes to the dividend. The new dividend is 11100.

 

Step 8: Find the new divisor that is 579 because 5799 x 9 = 52191.

 

Step 9: Subtracting 52191 from 11100 results in 889.

 

Step 10: Now the quotient is 57.9.

 

Step 11: Continue these steps until we get two numbers after the decimal point or until the remainder is zero. So the square root of √3360 is approximately 57.93.

Professor Greenline from BrightChamps

Square Root of 3360 by Approximation Method

The approximation method is another method for finding square roots, and it is an easy method to find the square root of a given number. Let us learn how to find the square root of 3360 using the approximation method.

 

Step 1: Find the closest perfect squares to √3360. The smallest perfect square less than 3360 is 3249 (57^2), and the largest perfect square more than 3360 is 3481 (59^2). √3360 falls between 57 and 59.

 

Step 2: Apply the formula: (Given number - smallest perfect square) ÷ (Greater perfect square - smallest perfect square) Using the formula: (3360 - 3249) ÷ (3481 - 3249) = 111 ÷ 232 ≈ 0.4784 Using the formula, we identified the decimal point of our square root. The next step is adding the initial integer to the decimal number: 57 + 0.4784 ≈ 57.93. So the square root of 3360 is approximately 57.93.

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Common Mistakes and How to Avoid Them in the Square Root of 3360

Students make mistakes while finding the square root, such as forgetting about the negative square root or skipping long division steps. Let us look at a few common mistakes that students make in detail.

Mistake 1

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Forgetting about the negative square root

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It is important to remember that a number has both positive and negative square roots. However, we typically use only the positive square root, as it is the required one in many practical situations.

 

For example, √50 = 7.07, but there is also -7.07, which should not be forgotten.

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Square Root of 3360 Examples

Ray, the Character from BrightChamps Explaining Math Concepts
Max, the Girl Character from BrightChamps

Problem 1

Can you help Max find the area of a square box if its side length is given as √3360?

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The area of the square is approximately 3360 square units.

Explanation

The area of the square = side^2.

The side length is given as √3360.

Area of the square = side^2 = √3360 x √3360 = 3360.

Therefore, the area of the square box is approximately 3360 square units.

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Max, the Girl Character from BrightChamps

Problem 2

A square-shaped building measuring 3360 square feet is built; if each of the sides is √3360, what will be the square feet of half of the building?

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1680 square feet

Explanation

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

Dividing 3360 by 2 = 1680.

So half of the building measures 1680 square feet.

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Max, the Girl Character from BrightChamps

Problem 3

Calculate √3360 x 5.

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Approximately 289.66

Explanation

First, find the square root of 3360, which is approximately 57.93.

The second step is to multiply 57.93 by 5.

So 57.93 x 5 ≈ 289.66.

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Max, the Girl Character from BrightChamps

Problem 4

What will be the square root of (3300 + 60)?

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The square root is approximately 58.

Explanation

To find the square root, find the sum of (3300 + 60).

3300 + 60 = 3360, and the square root of 3360 is approximately 58.

Therefore, the square root of (3300 + 60) is approximately 58.

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Max, the Girl Character from BrightChamps

Problem 5

Find the perimeter of the rectangle if its length ‘l’ is √3360 units and the width ‘w’ is 60 units.

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The perimeter of the rectangle is approximately 235.86 units.

Explanation

Perimeter of the rectangle = 2 × (length + width) Perimeter = 2 × (√3360 + 60) Perimeter = 2 × (57.93 + 60) = 2 × 117.93 ≈ 235.86 units.

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FAQ on Square Root of 3360

1.What is √3360 in its simplest form?

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2.Mention the factors of 3360.

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3.Calculate the square of 3360.

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4.Is 3360 a prime number?

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5.3360 is divisible by?

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6.How does learning Algebra help students in Oman make better decisions in daily life?

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7.How can cultural or local activities in Oman support learning Algebra topics such as Square Root of 3360?

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8.How do technology and digital tools in Oman support learning Algebra and Square Root of 3360?

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9.Does learning Algebra support future career opportunities for students in Oman?

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Professor Greenline from BrightChamps

Important Glossaries for the Square Root of 3360

  • Square root: A square root is the inverse operation of squaring a number. Example: 4^2 = 16, and the inverse is the square root, √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 ≠ 0.

 

  • Principal square root: The positive square root of a number, which is used in most practical applications. It is the most commonly referenced square root.

 

  • Perfect square: A number that is the square of an integer. Example: 36 is a perfect square because it is 6^2.

 

  • Long division method: A method used to find the square root of a number that is not a perfect square, involving a series of steps to approximate the root.
Professor Greenline from BrightChamps

About BrightChamps in Oman

At BrightChamps, we understand algebra as more than symbols—it’s a key to unlocking many opportunities! Our mission is to help children across Oman gain important math skills, focusing today on the Square Root of 3360 with special attention to square roots—in an engaging, lively, and easy-to-follow manner. Whether your child is measuring how fast a roller coaster moves at Oman’s Dreamland Aqua Park, tracking local football scores, or managing their allowance for the latest gadgets, mastering algebra gives them confidence for everyday tasks. Our hands-on lessons make learning simple and fun. Because children in Oman learn differently, we adapt lessons to fit each learner’s style. From Muscat’s vibrant city life to beautiful natural landscapes, BrightChamps brings math to life, making it exciting throughout Oman. Let’s make square roots a joyful part of every child’s math journey!
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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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Max, the Girl Character from BrightChamps

Fun Fact

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

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