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Last updated on May 26th, 2025

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Square Root of 2664

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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 2664.

Square Root of 2664 for Singaporean Students
Professor Greenline from BrightChamps

What is the Square Root of 2664?

The square root is the inverse of the square of the number. 2664 is not a perfect square. The square root of 2664 is expressed in both radical and exponential form. In the radical form, it is expressed as √2664, whereas (2664)^(1/2) in the exponential form. √2664 ≈ 51.627, 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 2664

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 2664 by Prime Factorization Method

The product of prime factors is the prime factorization of a number. Now let us look at how 2664 is broken down into its prime factors.

 

Step 1: Finding the prime factors of 2664 Breaking it down, we get 2 x 2 x 2 x 3 x 3 x 37: 2^3 x 3^2 x 37

 

Step 2: Now we found out the prime factors of 2664. The second step is to make pairs of those prime factors. Since 2664 is not a perfect square, the digits of the number can’t be grouped in a perfect pair.

 

Therefore, calculating 2664 using prime factorization directly is not feasible.

Professor Greenline from BrightChamps

Square Root of 2664 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 with, we need to group the numbers from right to left. In the case of 2664, we need to group it as 64 and 26.

 

Step 2: Now we need to find n whose square is closest to 26. We can use n = 5 because 5 x 5 = 25 is less than 26. Now the quotient is 5, and after subtracting 25 from 26, the remainder is 1.

 

Step 3: Now let us bring down 64, which is the new dividend. Add the old divisor with the same number 5 + 5, giving us 10, which will be our new divisor.

 

Step 4: The new divisor will be 10, and we need to find a digit to replace the blank in 10_ that, when multiplied by itself, results in a product less than or equal to 164.

 

Step 5: The next step is finding 10n × n ≤ 164. Let us consider n as 1, now 101 x 1 = 101.

 

Step 6: Subtract 101 from 164, the difference is 63, and the quotient is 51.

 

Step 7: Since the remainder is less than the divisor, we add a decimal point and bring down two zeros to make the dividend 6300.

 

Step 8: Now, the new divisor is 102, and we continue the process as with integers, finding the next digit of the quotient. Continue doing these steps until we get the desired number of decimal places.

 

So the approximate square root of √2664 is 51.627.

Professor Greenline from BrightChamps

Square Root of 2664 by Approximation Method

The approximation method is another method for finding the square roots. It is an easy method to find the square root of a given number. Now let us learn how to find the square root of 2664 using the approximation method.

 

Step 1: Now we have to find the closest perfect square to √2664. The closest perfect squares around 2664 are 2601 (51^2) and 2704 (52^2). √2664 falls somewhere between 51 and 52.

 

Step 2: Now we need to apply the formula: (Given number - smallest perfect square) ÷ (Greater perfect square - smallest perfect square) Going by the formula (2664 - 2601) ÷ (2704 - 2601) = 63 ÷ 103 ≈ 0.611 Using the formula, we identified the decimal point of our square root. The next step is adding the value we got initially to the decimal number, which is 51 + 0.611 = 51.611.

 

Thus, the approximate square root of 2664 is 51.611.

Max Pointing Out Common Math Mistakes

Common Mistakes and How to Avoid Them in the Square Root of 2664

Students do make mistakes while finding the square root, like forgetting about the negative square root or skipping long division methods, etc. Now let us look at a few of those mistakes that students tend to make 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 does have both positive and negative square roots. However, we typically consider only the positive square root, as it is the required one for most practical purposes.

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

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Square Root of 2664 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 if its side length is given as √2664?

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The area of the square is approximately 2664 square units.

Explanation

The area of a square = side^2.

The side length is given as √2664.

Area of the square = side^2

= √2664 × √2664

= 2664.

Therefore, the area of the square is approximately 2664 square units.

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

Problem 2

A square-shaped building measuring 2664 square feet is built. If each of the sides is √2664, what will be the square feet of half of the building?

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

1332 square feet

Explanation

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

Dividing 2664 by 2 = 1332.

So half of the building measures 1332 square feet.

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

Problem 3

Calculate √2664 × 5.

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

Approximately 258.135

Explanation

The first step is to find the square root of 2664, which is approximately 51.627.

The second step is to multiply 51.627 by 5.

So 51.627 × 5 ≈ 258.135.

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Max, the Girl Character from BrightChamps

Problem 4

What will be the square root of (2664 + 40)?

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

The square root is approximately 52.

Explanation

To find the square root, we need to find the sum of (2664 + 40).

2664 + 40 = 2704, and then √2704 = 52.

Therefore, the square root of (2664 + 40) is ±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 √2664 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 179.254 units.

Explanation

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

Perimeter = 2 × (√2664 + 38)

= 2 × (51.627 + 38)

= 2 × 89.627

= 179.254 units.

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

FAQ on Square Root of 2664

1.What is √2664 in its simplest form?

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2.Mention the factors of 2664.

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3.Calculate the square of 2664.

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4.Is 2664 a prime number?

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5.2664 is divisible by?

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

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7.How can cultural or local activities in Singapore support learning Algebra topics such as Square Root of 2664?

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8.How do technology and digital tools in Singapore support learning Algebra and Square Root of 2664?

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

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Professor Greenline from BrightChamps

Important Glossaries for the Square Root of 2664

  • 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 the positive square root that is most commonly used, known as the principal square root.
     
  • Prime factorization: A method of expressing a number as the product of its prime factors.
     
  • Decimal approximation: An estimate of an irrational number's value using decimals, often used when an exact expression is complex or impossible to obtain in simple form.
Professor Greenline from BrightChamps

About BrightChamps in Singapore

At BrightChamps, we see algebra as more than just symbols—it opens up a world of opportunities! We’re committed to helping children across Singapore develop essential math skills, focusing today on the Square Root of 2664 with a special focus on understanding square roots—in an engaging, lively, and simple way. Whether your child is figuring out how fast a roller coaster speeds at Universal Studios Singapore, keeping track of football match scores, or managing their allowance for the newest gadgets, mastering algebra boosts their confidence in daily life. Our interactive lessons make learning fun and accessible. Because kids in Singapore learn in various ways, we customize our teaching to fit each child’s style. From bustling city streets to scenic gardens, BrightChamps makes math come alive throughout Singapore. Let’s make square roots an exciting 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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