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Last updated on May 26th, 2025

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Square Root of 3604

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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 3604.

Square Root of 3604 for UAE Students
Professor Greenline from BrightChamps

What is the Square Root of 3604?

The square root is the inverse of the square of a number. 3604 is not a perfect square. The square root of 3604 is expressed in both radical and exponential form. In the radical form, it is expressed as √3604, whereas (3604)^(1/2) in the exponential form. √3604 ≈ 60.04, 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.

Professor Greenline from BrightChamps

Finding the Square Root of 3604

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 3604 by Prime Factorization Method

The product of prime factors is the prime factorization of a number. Now let us look at how 3604 is broken down into its prime factors.

 

Step 1: Finding the prime factors of 3604 Breaking it down, we get 2 x 2 x 13 x 13 x 7: 2^2 x 13^2 x 7

 

Step 2: Now we found out the prime factors of 3604. Since 3604 is not a perfect square, the digits of the number can’t be grouped into complete pairs.

 

Therefore, calculating 3604 using prime factorization alone involves further steps.

Professor Greenline from BrightChamps

Square Root of 3604 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: Group the numbers from right to left. For 3604, we group it as 04 and 36.

 

Step 2: Find n whose square is closest to 36. We can say n is ‘6’ because 6 x 6 = 36. The quotient is 6, and the remainder is 0 after subtracting 36 from 36.

 

Step 3: Bring down 04, which is the new dividend. Add the old divisor with the quotient, 6 + 6, to get 12, which will be our new divisor.

 

Step 4: The new divisor will be the sum of the current divisor and a number. We need to find n such that 12n × n ≤ 04.

 

Step 5: Since 12 x 0 x 0 = 0, subtract 0 from 04 to get a remainder of 4. The quotient is now 60.

 

Step 6: Since the dividend is less than the divisor, add a decimal point. Now the new dividend is 400.

 

Step 7: Find a new divisor such that 120n x n ≤ 400. If n = 3, then 120 x 3 x 3 = 360.

 

Step 8: Subtract 360 from 400 to get a remainder of 40. The quotient is 60.3.

 

Step 9: Continue until the desired precision is achieved.

 

The square root of √3604 ≈ 60.04.

Professor Greenline from BrightChamps

Square Root of 3604 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 3604 using the approximation method.

 

Step 1: Find the closest perfect squares of √3604. The smallest perfect square less than 3604 is 3600, and the largest perfect square greater than 3604 is 3721. √3604 falls somewhere between 60 and 61.

 

Step 2: Apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Formula: (3604 - 3600) / (3721 - 3600) = 4 / 121 ≈ 0.033. Using the formula, we add the value we got initially to the decimal number: 60 + 0.033 ≈ 60.04.

 

So the square root of 3604 is approximately 60.04.

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Common Mistakes and How to Avoid Them in the Square Root of 3604

Students might make mistakes while finding the square root, such as forgetting the negative square root or skipping steps in the long division method. Now let us look at a few common mistakes in detail.

Mistake 1

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Forgetting about the negative square root

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It is important to make students aware that a number has both positive and negative square roots. However, we generally use the principal (positive) square root.

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

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Square root of 3604 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 √2604?

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The area of the square is approximately 2603.8 square units.

Explanation

The area of the square = side^2.

The side length is given as √2604.

Area of the square = side^2 = √2604 x √2604 ≈ 51.03 x 51.03 = 2603.8.

Therefore, the area of the square box is approximately 2603.8 square units.

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Max, the Girl Character from BrightChamps

Problem 2

A square-shaped building measuring 3604 square feet is built; if each of the sides is √3604, what will be the square feet of half of the building?

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1802 square feet

Explanation

Since the building is square-shaped, dividing the area by 2 gives the area of half the building.

Dividing 3604 by 2 = 1802.

So half of the building measures 1802 square feet.

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Max, the Girl Character from BrightChamps

Problem 3

Calculate √3604 x 5.

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Approximately 300.2

Explanation

First, find the square root of 3604, which is approximately 60.04.

Then multiply 60.04 by 5.

So, 60.04 x 5 ≈ 300.2.

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Max, the Girl Character from BrightChamps

Problem 4

What will be the square root of (3604 + 16)?

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The square root is approximately 61.52.

Explanation

To find the square root, first find the sum of (3604 + 16).

3604 + 16 = 3620, and then √3620 ≈ 61.52.

Therefore, the square root of (3604 + 16) is approximately ±61.52.

Max from BrightChamps Praising Clear Math Explanations
Max, the Girl Character from BrightChamps

Problem 5

Find the perimeter of the rectangle if its length ‘l’ is √3604 units and the width ‘w’ is 38 units.

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"

The perimeter of the rectangle is approximately 196.08 units.

Explanation

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

Perimeter = 2 × (√3604 + 38)

= 2 × (60.04 + 38)

= 2 × 98.04

≈ 196.08 units.

Max from BrightChamps Praising Clear Math Explanations
Ray Thinking Deeply About Math Problems

FAQ on Square Root of 3604

1.What is √3604 in its simplest form?

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2.Mention the factors of 3604.

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3.Calculate the square of 3604.

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4.Is 3604 a prime number?

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5.3604 is divisible by?

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6.How does learning Algebra help students in United Arab Emirates make better decisions in daily life?

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7.How can cultural or local activities in United Arab Emirates support learning Algebra topics such as Square Root of 3604?

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8.How do technology and digital tools in United Arab Emirates support learning Algebra and Square Root of 3604?

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9.Does learning Algebra support future career opportunities for students in United Arab Emirates?

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Professor Greenline from BrightChamps

Important Glossaries for the Square Root of 3604

  • 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 is more commonly used in real-world applications, known as the principal square root.
     
  • Prime factorization: Prime factorization is expressing a number as the product of its prime factors. For example, prime factorization of 18 is 2 x 3 x 3.
     
  • Long division method: A method used to find the square root of non-perfect squares by dividing the number into pairs of digits starting from the decimal point.
Professor Greenline from BrightChamps

About BrightChamps in United Arab Emirates

At BrightChamps, we know algebra is more than symbols—it opens doors to endless possibilities! We’re dedicated to helping kids throughout the UAE develop crucial math skills, focusing today on the Square Root of 3604 with a special focus on square roots—in an enjoyable, engaging, and easy-to-understand way. Whether your child is figuring out the speed of a roller coaster at Dubai Parks and Resorts, keeping track of local football scores, or budgeting their allowance for the latest gadgets, mastering algebra gives them confidence for everyday situations. Our interactive lessons make learning both fun and simple. Because kids in the UAE learn in varied ways, we customize our teaching to fit each child’s needs. From Dubai’s soaring skyscrapers to Abu Dhabi’s cultural heritage, BrightChamps brings math alive, making it relevant and exciting throughout the UAE. 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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