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Last updated on May 26th, 2025

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Square Root of 639

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If a number is multiplied by itself, the result is a square. The inverse of squaring a number is finding its square root. Square roots are used in various fields such as engineering, finance, and more. Here, we will discuss the square root of 639.

Square Root of 639 for Saudi Students
Professor Greenline from BrightChamps

What is the Square Root of 639?

The square root is the inverse operation of squaring a number. 639 is not a perfect square. The square root of 639 can be expressed in both radical and exponential forms. In radical form, it is expressed as √639, whereas in exponential form it is written as (639)^(1/2). The value of √639 is approximately 25.27, which is an irrational number because it cannot be expressed as a simple fraction p/q, where p and q are integers and q ≠ 0.

Professor Greenline from BrightChamps

Finding the Square Root of 639

The prime factorization method is typically used for perfect squares. For non-perfect squares like 639, methods such as the long division method and approximation method are used. Let us now explore these methods:

 

  • Prime factorization method
  • Long division method
  • Approximation method
Professor Greenline from BrightChamps

Square Root of 639 by Prime Factorization Method

Prime factorization involves expressing a number as a product of its prime factors. Let's break down 639 into its prime factors:

 

Step 1: Finding the prime factors of 639 Breaking it down, we get 3 x 3 x 71: 3^2 x 71

 

Step 2: We found the prime factors of 639. Since 639 is not a perfect square, the digits of the number cannot be grouped into pairs.

 

Therefore, calculating √639 using prime factorization does not yield an exact result.

Professor Greenline from BrightChamps

Square Root of 639 by Long Division Method

The long division method is used for non-perfect squares. Here’s how to find the square root using this method, step by step:

 

Step 1: Group the digits of 639 from right to left. In this case, we have 39 and 6.

 

Step 2: Find n such that n^2 is less than or equal to 6. Here, n is 2 because 2^2 = 4, and 4 ≤ 6. The quotient is 2, and the remainder is 6 - 4 = 2.

 

Step 3: Bring down the next pair, 39, making the new dividend 239. Double the quotient (2), giving us 4, which will be part of our new divisor.

 

Step 4: Find a digit x such that 4x × x ≤ 239. Let x be 5, as 45 × 5 = 225, and 225 ≤ 239.

 

Step 5: Subtract 225 from 239 to get a remainder of 14. The quotient is now 25.

 

Step 6: Since the remainder is less than the new divisor, add a decimal point to the quotient. Bring down a pair of zeros to the dividend, making it 1400.

 

Step 7: Double the quotient (25) to get 50, then find x such that 50x × x ≤ 1400. Let x be 2, giving 502 × 2 = 1004.

 

Step 8: Subtract 1004 from 1400 to get 396. The quotient becomes 25.2.

 

Step 9: Continue this process until you reach the desired decimal precision.

 

So the square root of √639 is approximately 25.27.

Professor Greenline from BrightChamps

Square Root of 639 by Approximation Method

The approximation method is a simpler approach to finding square roots. Let's find the square root of 639 using this method:

 

Step 1: Identify the nearest perfect squares around 639. Here, 625 (25^2) and 676 (26^2) are the closest.

 

Step 2: Apply the formula: \( \frac{639 - 625}{676 - 625} = \frac{14}{51} \approx 0.27 \) Using this formula, we find the decimal part of our square root. Add this to the integer part, giving 25 + 0.27 = 25.27.

 

Therefore, the square root of 639 is approximately 25.27.

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Common Mistakes and How to Avoid Them in the Square Root of 639

Students often make errors when finding square roots, such as forgetting about the negative square root, skipping steps in the long division method, etc. Let's explore some common mistakes and how to avoid them.

Mistake 1

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Forgetting about the negative square root

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It is crucial to remember that every positive number has both a positive and a negative square root. However, we typically consider only the principal (positive) square root in practical applications.

For example, √50 = 7.07, but there is also -7.07.

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Square Root of 639 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 √639?

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The area of the square is approximately 639 square units.

Explanation

The area of a square = side^2.

The side length is given as √639.

Area of the square = (√639)^2 = 639.

Therefore, the area of the square box is approximately 639 square units.

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Max, the Girl Character from BrightChamps

Problem 2

A square-shaped building measuring 639 square feet is built; if each of the sides is √639, what will be the square feet of half of the building?

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319.5 square feet

Explanation

Since the building is square-shaped, divide the total area by 2 to find half of it.

639 ÷ 2 = 319.5

So half of the building measures 319.5 square feet.

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Max, the Girl Character from BrightChamps

Problem 3

Calculate √639 x 5.

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Approximately 126.35

Explanation

First, find the square root of 639, which is approximately 25.27.

Then, multiply 25.27 by 5.

So, 25.27 × 5 = 126.35.

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Max, the Girl Character from BrightChamps

Problem 4

What will be the square root of (639 + 11)?

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The square root is approximately 26.

Explanation

To find the square root, first compute the sum of 639 + 11.

639 + 11 = 650.

The square root of 650 is approximately 25.5, rounded to 26 for simplicity.

Therefore, the square root of (639 + 11) is approximately ±26.

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Max, the Girl Character from BrightChamps

Problem 5

Find the perimeter of the rectangle if its length ‘l’ is √639 units and the width ‘w’ is 38 units.

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The perimeter of the rectangle is approximately 126.54 units.

Explanation

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

Perimeter = 2 × (√639 + 38)

≈ 2 × (25.27 + 38)

= 2 × 63.27

= 126.54 units.

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FAQ on Square Root of 639

1.What is √639 in its simplest form?

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2.Mention the factors of 639.

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3.Calculate the square of 639.

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4.Is 639 a prime number?

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5.639 is divisible by?

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

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7.How can cultural or local activities in Saudi Arabia support learning Algebra topics such as Square Root of 639?

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8.How do technology and digital tools in Saudi Arabia support learning Algebra and Square Root of 639?

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

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Professor Greenline from BrightChamps

Important Glossaries for the Square Root of 639

  • Square root: A square root is the inverse operation of squaring a number. For example, if 4^2 = 16, then √16 = 4.
     
  • Irrational number: An irrational number cannot be expressed as a simple fraction of two integers. For example, √2 is irrational.
     
  • Principal square root: The principal square root is the non-negative square root of a number. For instance, the principal square root of 16 is 4.
     
  • Long division method: A technique used to find square roots of non-perfect squares by performing division operations iteratively.
     
  • Approximation method: A method to estimate the square root of a number by comparing it to nearby perfect squares.
Professor Greenline from BrightChamps

About BrightChamps in Saudi Arabia

At BrightChamps, we recognize algebra as more than just symbols—it’s a key to unlock countless opportunities! Our goal is to help children across Saudi Arabia gain important math skills, focusing today on the Square Root of 639 with special attention to square roots—in a way that’s engaging, lively, and easy to grasp. Whether your child is calculating the speed of a roller coaster at Riyadh’s Al Hokair Land, following scores at local football matches, or managing their allowance for the latest gadgets, mastering algebra boosts their confidence for daily challenges. Our interactive lessons make learning accessible and fun. Since children in Saudi Arabia learn in different ways, we tailor lessons to suit each learner. From Riyadh’s bustling streets to Jeddah’s historic landmarks, BrightChamps brings math to life, making it exciting and relevant all over Saudi Arabia. Let’s make square roots a fun part of every child’s math adventure!
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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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