127 LearnersLast updated on May 26th, 2025
Square Root of 666
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.
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.
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
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.
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.
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
Forgetting about the negative square root
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.
Mistake 2
Not adding the square root symbol in proper places
Incorrect use of the square root symbol is another common mistake. To resolve this, students need to understand that simplifying the numbers inside the square root is essential before moving to the next step.
For example: √(12+24) = √12 + √24 is incorrect. The correct method is √(12+24) = √36.
Mistake 3
Not finding the correct value of a non-perfect square
Students must first simplify the numbers inside the square root to avoid mistakes in identifying the approximate value.
For example, √50 = 7 is incorrect; the correct answer is √50 ≈ 7.071067.
Mistake 4
Confusing the square root symbol with the cube root
Students need to be taught the difference between cube roots and square roots to avoid confusion.
For example, √50 and ∛50 are different.
Mistake 5
Mistakes in the long division method
Finding a square root using the long division method involves several steps. Many students might accidentally skip a step, leading to an incorrect answer. This can happen during subtraction or other steps.
Square Root of 666 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √666?
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.
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?
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.
Problem 3
Calculate √666 x 5.
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.
Problem 4
What will be the square root of (660 + 6)?
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.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √666 units and the width ‘w’ is 38 units.
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.
FAQ on Square Root of 666
1.What is √666 in its simplest form?
2.What are the factors of 666?
3.Calculate the square of 666.
4.Is 666 a prime number?
5.What is 666 divisible by?
6.How does learning Algebra help students in Saudi Arabia make better decisions in daily life?
7.How can cultural or local activities in Saudi Arabia support learning Algebra topics such as Square Root of 666?
8.How do technology and digital tools in Saudi Arabia support learning Algebra and Square Root of 666?
9.Does learning Algebra support future career opportunities for students in Saudi Arabia?
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.
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About BrightChamps in Saudi Arabia
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.
Fun Fact
: He loves to play the quiz with kids through algebra to make kids love it.
