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Last updated on May 26th, 2025

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Square Root of 641

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If a number is multiplied by itself, the result is a square. The inverse operation is finding the square root. The square root is used in fields such as engineering, physics, and finance. Here, we will discuss the square root of 641.

Square Root of 641 for UAE Students
Professor Greenline from BrightChamps

What is the Square Root of 641?

The square root is the inverse operation of squaring a number. 641 is not a perfect square. The square root of 641 can be expressed in both radical and exponential forms. In radical form, it is expressed as √641, whereas in exponential form, it is (641)^(1/2). The square root of 641 is approximately 25.31798, which is an irrational number because it cannot be expressed as a fraction p/q, where p and q are integers and q ≠ 0.

Professor Greenline from BrightChamps

Finding the Square Root of 641

The prime factorization method is used for perfect square numbers. However, for non-perfect square numbers, methods like the 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 641 by Prime Factorization Method

The product of prime factors is the prime factorization of a number. Now let us look at how 641 is broken down into its prime factors:

 

Step 1: Finding the prime factors of 641 Since 641 is a prime number, it cannot be broken down into smaller prime factors.

 

Step 2: Since 641 is not a perfect square and is a prime number, calculating its square root using prime factorization is not applicable.

Professor Greenline from BrightChamps

Square Root of 641 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 numbers 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 digits of 641 from right to left. In this case, we have 6 and 41.

 

Step 2: Find n such that n^2 is less than or equal to 6. The closest n is 2, since 2^2 = 4. Place 2 above the 6 as the first digit of the quotient.

 

Step 3: Subtract 4 from 6, and bring down 41 to form the new dividend 241.

 

Step 4: Double the current quotient (2), which is 4, and use it as the new divisor's first digit.

 

Step 5: Find a digit d such that (40 + d) * d ≤ 241. The value of d is 6, since 46 * 6 = 276, which is greater than 241, but 45 * 5 = 225, which is less than 241.

 

Step 6: Place 5 next to 2 in the quotient, making it 25. Subtract 225 from 241, leaving a remainder of 16.

 

Step 7: Bring down two zeros to form 1600 and continue the process to get a more accurate result.

 

Step 8: This process is continued until the desired precision is reached.

 

The square root of 641 is approximately 25.31.

Professor Greenline from BrightChamps

Square Root of 641 by Approximation Method

The approximation method is an easy way to find the square roots of numbers, especially when they are not perfect squares. Let us learn how to find the square root of 641 using the approximation method:

 

Step 1: Identify the perfect squares closest to 641. The closest perfect squares are 625 (25^2) and 676 (26^2). √641 falls between 25 and 26.

 

Step 2: Apply the formula: (Given number - smaller perfect square) / (Larger perfect square - smaller perfect square). Using the formula: (641 - 625) / (676 - 625) = 16 / 51 ≈ 0.314. Step 3: Add this decimal to the smaller integer, 25 + 0.314 = 25.314.

 

Thus, the approximate square root of 641 is 25.314.

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Common Mistakes and How to Avoid Them in the Square Root of 641

Students often make mistakes while finding the square root, such as overlooking the negative square root. It's also common to skip 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 usually consider only the positive square root as it is often the required one.

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

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Square Root of 641 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 √641?

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The area of the square is 641 square units.

Explanation

The area of the square = side^2.

The side length is given as √641.

Area of the square = side^2 = √641 x √641 = 641.

Therefore, the area of the square box is 641 square units.

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Max, the Girl Character from BrightChamps

Problem 2

A square-shaped building measuring 641 square feet is built; if each of the sides is √641, what will be the square feet of half of the building?

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320.5 square feet

Explanation

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

Dividing 641 by 2 gives us 320.5.

So half of the building measures 320.5 square feet.

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Max, the Girl Character from BrightChamps

Problem 3

Calculate √641 x 5.

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126.5899

Explanation

The first step is to find the square root of 641, which is approximately 25.31798.

The second step is to multiply 25.31798 by 5.

So, 25.31798 x 5 ≈ 126.5899.

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Max, the Girl Character from BrightChamps

Problem 4

What will be the square root of (625 + 16)?

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

The square root is 26.

Explanation

To find the square root, we need to find the sum of (625 + 16).

625 + 16 = 641, and √641 ≈ 25.31798.

However, using the perfect squares, 625 + 16 = 641, where the closest perfect square is 676, √676 = 26.

Therefore, the square root of (625 + 16) is approximately 26.

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Max, the Girl Character from BrightChamps

Problem 5

Find the perimeter of a rectangle if its length ‘l’ is √641 units and the width ‘w’ is 38 units.

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The perimeter of the rectangle is approximately 126.63596 units.

Explanation

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

Perimeter = 2 × (√641 + 38)

≈ 2 × (25.31798 + 38)

≈ 2 × 63.31798

≈ 126.63596 units.

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FAQ on Square Root of 641

1.What is √641 in its simplest form?

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2.Is 641 a prime number?

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3.Calculate the square of 641.

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4.What are the closest perfect squares to 641?

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5.What is √641 rounded to two decimal places?

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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 641?

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8.How do technology and digital tools in United Arab Emirates support learning Algebra and Square Root of 641?

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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 641

  • Square root: A square root is the inverse operation of squaring a number. For example, 5^2 = 25, and the square root is √25 = 5.
     
  • Irrational number: An irrational number is a number that cannot be expressed as a simple fraction, such as √641.
     
  • Principal square root: The principal square root is the non-negative square root of a number, often used in calculations.
     
  • Prime number: A prime number has exactly two distinct positive divisors: 1 and itself. For example, 641 is a prime number.
     
  • Long division method: A technique used to find the square root of a number by iteratively dividing and averaging.
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 641 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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