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Last updated on May 26th, 2025

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Square Root of 666

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If a number is multiplied by the same number, the result is a square. The inverse of squaring a number is finding its square root. The square root is used in fields such as vehicle design, finance, etc. Here, we will discuss the square root of 666.

Square Root of 666 for Saudi Students
Professor Greenline from BrightChamps

What is the Square Root of 666?

The square root is the inverse operation of squaring a number. 666 is not a perfect square. The square root of 666 can be expressed in both radical and exponential forms. In radical form, it is expressed as √666, whereas in exponential form, it is (666)^(1/2). √666 ≈ 25.80698, 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 666

The prime factorization method is used for perfect square numbers. However, for non-perfect square numbers like 666, the long division method and approximation method are used. Let us now learn the following methods:

 

  • Long division method
  • Approximation method
Professor Greenline from BrightChamps

Square Root of 666 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, group the numbers from right to left. In the case of 666, group it as 66 and 6.

 

Step 2: Find n whose square is closest to 6. We can say n is ‘2’ because 2×2 = 4, which is less than 6. The quotient is 2, and after subtracting 4 from 6, the remainder is 2.

 

Step 3: Bring down 66, making the new dividend 266. Add the old divisor with itself: 2 + 2 = 4, which will be our new divisor.

 

Step 4: Now, find the largest digit n such that 4n×n ≤ 266. Let n be 6; thus, 46×6 = 276, which is greater than 266. Try n = 5: 45×5 = 225.

 

Step 5: Subtract 225 from 266, and the difference is 41. The quotient is 25.

 

Step 6: Since the dividend is less than the divisor, add a decimal point and two zeroes to the dividend, making it 4100.

 

Step 7: Find a new divisor: 255. Since 255×5 = 1275 is less than 4100, choose 5.

 

Step 8: Subtract 1275 from 4100 to get 2825. The new quotient is 25.8. Continue this process until the desired accuracy is achieved.

 

Thus, the square root of √666 ≈ 25.806.

Professor Greenline from BrightChamps

Square Root of 666 by Approximation Method

The approximation method is another way to find square roots. It is an easy method to find the square root of a given number. Now let's learn how to find the square root of 666 using the approximation method.

 

Step 1: Find the closest perfect squares of √666. The smallest perfect square less than 666 is 625, and the largest perfect square greater than 666 is 676. √666 falls between 25 and 26.

 

Step 2: Apply the formula: (Given number - smallest perfect square) / (Largest perfect square - smallest perfect square). Using the formula: (666 - 625) / (676 - 625) = 41 / 51 ≈ 0.8039. Add this decimal to the lower bound: 25 + 0.8039 ≈ 25.804.

 

Thus, the approximate square root of 666 is 25.804.

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Common Mistakes and How to Avoid Them in the Square Root of 666

Students often make mistakes while finding the square root, such as forgetting about the negative square root or skipping the long division method. Let's 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 for students to be aware that a number has both positive and negative square roots. However, we typically focus on the positive square root, as it is the one most often required.

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

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Square Root of 666 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 √666?

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The area of the square is approximately 666 square units.

Explanation

The area of a square = side².

The side length is given as √666.

Area of the square = (√666)² = 666 square units.

Therefore, the area of the square box is approximately 666 square units.

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Max, the Girl Character from BrightChamps

Problem 2

A square-shaped building measuring 666 square feet is built; if each side is √666, what will be the square feet of half of the building?

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333 square feet

Explanation

Since the building is square-shaped, divide the given area by 2.

Dividing 666 by 2 gives us 333.

So, half of the building measures 333 square feet.

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Max, the Girl Character from BrightChamps

Problem 3

Calculate √666 x 5.

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Approximately 129.03

Explanation

First, find the square root of 666, which is approximately 25.80698.

Then, multiply 25.80698 by 5:

25.80698 x 5 ≈ 129.03.

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Max, the Girl Character from BrightChamps

Problem 4

What will be the square root of (660 + 6)?

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The square root is approximately 25.80698.

Explanation

To find the square root, sum 660 + 6 = 666.

Then, √666 ≈ 25.80698.

Therefore, the square root of (660 + 6) is approximately ±25.80698.

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Max, the Girl Character from BrightChamps

Problem 5

Find the perimeter of the rectangle if its length ‘l’ is √666 units and the width ‘w’ is 38 units.

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The perimeter of the rectangle is approximately 127.61 units.

Explanation

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

Perimeter = 2 × (√666 + 38)

≈ 2 × (25.80698 + 38)

≈ 2 × 63.80698

≈ 127.61 units.

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FAQ on Square Root of 666

1.What is √666 in its simplest form?

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2.What are the factors of 666?

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3.Calculate the square of 666.

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4.Is 666 a prime number?

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5.What is 666 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 666?

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8.How do technology and digital tools in Saudi Arabia support learning Algebra and Square Root of 666?

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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 666

  • Square root: The square root is the inverse of squaring a number. Example: 4² = 16, and the inverse is √16 = 4.
     
  • Irrational number: An irrational number cannot be written as a simple fraction (p/q). It has an infinite, non-repeating decimal expansion.
     
  • Principal square root: The positive square root of a number; typically the one we use unless stated otherwise.
     
  • Long division method: A step-by-step method used to calculate square roots, especially for non-perfect squares.
     
  • Approximation method: Estimating the square root of a number using nearby perfect squares and linear interpolation.
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 666 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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