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Last updated on May 26th, 2025

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Square Root of 672

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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 fields such as vehicle design, finance, etc. Here, we will discuss the square root of 672.

Square Root of 672 for Singaporean Students
Professor Greenline from BrightChamps

What is the Square Root of 672?

The square root is the inverse of the square of the number. 672 is not a perfect square. The square root of 672 is expressed in both radical and exponential form. In the radical form, it is expressed as √672, whereas (672)^(1/2) in the exponential form. √672 ≈ 25.922, 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 672

The prime factorization method is used for perfect square numbers. However, the prime factorization method is not used for non-perfect square numbers, where 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 672 by Prime Factorization Method

The product of prime factors is the prime factorization of a number. Now let us look at how 672 is broken down into its prime factors:

 

Step 1: Finding the prime factors of 672 Breaking it down, we get 2 x 2 x 2 x 2 x 3 x 7: 2^4 x 3 x 7

 

Step 2: Now we found out the prime factors of 672. The second step is to make pairs of those prime factors. Since 672 is not a perfect square, the digits of the number can’t be grouped into pairs.

 

Therefore, calculating 672 using prime factorization is impossible for finding an exact square root.

Professor Greenline from BrightChamps

Square Root of 672 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 672, we need to group it as 72 and 6.

 

Step 2: Now we need to find n whose square is closest to 6. We can say n is '2' because 2 x 2 = 4 is lesser than or equal to 6. Now the quotient is 2, and after subtracting 4 from 6, the remainder is 2.

 

Step 3: Now let us bring down 72, which is the new dividend. Add the old divisor with the same number: 2 + 2 = 4, which will be our new divisor.

 

Step 4: The new divisor will be followed by finding the value of n such that 4n x n ≤ 272.

 

Step 5: The next step is finding 4n x n ≤ 272. Let us consider n as 6; now 46 x 6 = 276, which is too large, so we try n as 5.

 

Step 6: Subtract 245 (45 x 5) from 272; the difference is 27, and the quotient is 25.

 

Step 7: Since the dividend is less than the divisor, we need to add a decimal point. Adding the decimal point allows us to add two zeroes to the dividend. Now the new dividend is 2700.

 

Step 8: We need to find the new divisor, which is 509 because 509 x 5 = 2545.

 

Step 9: Subtracting 2545 from 2700, we get the result 155.

 

Step 10: Now the quotient is 25.9.

 

Step 11: Continue doing these steps until we get two numbers after the decimal point. Suppose there are no decimal values; continue until the remainder is zero.

 

So the square root of √672 is approximately 25.92.

Professor Greenline from BrightChamps

Square Root of 672 by Approximation Method

The approximation method is another method for finding 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 672 using the approximation method.

 

Step 1: Now we have to find the closest perfect squares of √672. The smallest perfect square less than 672 is 625, and the largest perfect square greater than 672 is 729. √672 falls somewhere between 25 and 26.

 

Step 2: Now we need to apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Going by the formula: (672 - 625) ÷ (729 - 625) = 47 ÷ 104 ≈ 0.452. 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 25 + 0.452 = 25.452, so the square root of 672 is approximately 25.92.

Max Pointing Out Common Math Mistakes

Common Mistakes and How to Avoid Them in the Square Root of 672

Students do make mistakes while finding the square root, such as forgetting about the negative square root, skipping long division steps, 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 will be taking only the positive square root, as it is the required one.

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

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Square Root of 672 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 √672?

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

The area of the square box is approximately 672 square units.

Explanation

The area of the square = side².

The side length is given as √672.

Area of the square = side² = √672 x √672 = 672.

Therefore, the area of the square box is approximately 672 square units.

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

Problem 2

A square-shaped building measuring 672 square feet is built. If each of the sides is √672, what will be the square feet of half of the building?

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

336 square feet

Explanation

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

Dividing 672 by 2 gives us 336.

So half of the building measures 336 square feet.

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Max, the Girl Character from BrightChamps

Problem 3

Calculate √672 x 5.

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

Approximately 129.61

Explanation

The first step is to find the square root of 672, which is approximately 25.92.

The second step is to multiply 25.92 by 5.

So 25.92 x 5 = approximately 129.61.

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

Problem 4

What will be the square root of (650 + 22)?

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The square root is approximately 25.92.

Explanation

To find the square root, we need to find the sum of (650 + 22).

650 + 22 = 672, and then √672 ≈ 25.92.

Therefore, the square root of (650 + 22) is approximately ±25.92.

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 √672 units and the width ‘w’ is 38 units.

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

We find the perimeter of the rectangle as approximately 127.84 units.

Explanation

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

Perimeter = 2 × (√672 + 38)

= 2 × (25.92 + 38)

= 2 × 63.92

≈ 127.84 units.

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

FAQ on Square Root of 672

1.What is √672 in its simplest form?

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2.Mention the factors of 672.

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3.Calculate the square of 672.

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4.Is 672 a prime number?

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5.672 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 672?

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8.How do technology and digital tools in Singapore support learning Algebra and Square Root of 672?

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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 672

  • Square root: A square root is the inverse of squaring a number. Example: 4^2 = 16, and the inverse of the square is the square root, i.e., √16 = 4.
     
  • Irrational number: An irrational number 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, the positive square root is usually taken as it is more commonly used in real-world applications. This is known as the principal square root.
     
  • Prime factorization: Prime factorization is expressing a number as a product of its prime factors.
     
  • Perfect square: A perfect square is a number that can be expressed as the product of an integer with itself. For example, 25 is a perfect square because it is 5 x 5.
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 672 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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