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Last updated on May 26th, 2025

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Square Root of 728

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If a number is multiplied by itself, the result is a square. The inverse of the square is a square root. The square root is used in various fields such as vehicle design, finance, etc. Here, we will discuss the square root of 728.

Square Root of 728 for US Students
Professor Greenline from BrightChamps

What is the Square Root of 728?

The square root is the inverse of the square of a number. 728 is not a perfect square. The square root of 728 can be expressed in both radical and exponential forms. In radical form, it is expressed as √728, whereas in exponential form it is (728)^(1/2). √728 ≈ 26.9737, which is an irrational number because it cannot be expressed as a ratio of two integers (p/q, where q ≠ 0).

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Finding the Square Root of 728

The prime factorization method is used for perfect square numbers. However, for non-perfect square numbers, methods like 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 728 by Prime Factorization Method

The product of prime factors is the prime factorization of a number. Now let us look at how 728 is broken down into its prime factors.

 

Step 1: Finding the prime factors of 728

 

Breaking it down, we get 2 × 2 × 2 × 91 = 2^3 × 7 × 13

 

Step 2: Now we found the prime factors of 728. The second step is to make pairs of those prime factors. Since 728 is not a perfect square, the digits of the number can’t be grouped in pairs. Therefore, calculating √728 using prime factorization alone is impractical.

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Square Root of 728 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 728, we need to group it as 28 and 7.

 

Step 2: Now we need to find n whose square is less than or equal to the first group (7). We can say n is ‘2’ because 2 × 2 = 4, which is less than or equal to 7. Now the quotient is 2; after subtracting 4 from 7, the remainder is 3.

 

Step 3: Now, bring down 28 to make it 328, which is the new dividend. Double the current quotient (2) to get 4, which becomes our new divisor (4_).

 

Step 4: Find a digit to fill in the blank (4_) such that the product of this new number and the same digit is less than or equal to 328.

 

Step 5: Continue this process until you achieve the desired precision. Using this method, you will find that √728 ≈ 26.97.

Professor Greenline from BrightChamps

Square Root of 728 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 728 using the approximation method.

 

Step 1: Find the closest perfect squares around 728. The smallest perfect square less than 728 is 676 (26^2), and the largest perfect square greater than 728 is 729 (27^2). Thus, √728 falls between 26 and 27.

 

Step 2: Apply the formula: (Given number - smaller perfect square) / (larger perfect square - smaller perfect square) (728 - 676) / (729 - 676) = 52/53 ≈ 0.9811 Add this decimal to the smaller square root: 26 + 0.9811 = 26.9811 Therefore, the square root of 728 is approximately 26.9811.

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Common Mistakes and How to Avoid Them in the Square Root of 728

Students often make mistakes while finding square roots, such as forgetting about the negative square root and skipping steps in the long division method. Let us 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 use only the positive square root, as it is more commonly required.

 

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

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Square Root of 728 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 √728?

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The area of the square is 728 square units.

Explanation

The area of the square = side^2.

The side length is given as √728.

Area of the square = side^2 = √728 × √728 = 728.

Therefore, the area of the square box is 728 square units.

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Max, the Girl Character from BrightChamps

Problem 2

A square-shaped building measuring 728 square feet is built. If each of the sides is √728, what will be the square feet of half of the building?

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364 square feet

Explanation

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

Dividing 728 by 2 gives us 364.

So, half of the building measures 364 square feet.

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Max, the Girl Character from BrightChamps

Problem 3

Calculate √728 × 5.

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134.87

Explanation

The first step is to find the square root of 728, which is approximately 26.97.

The second step is to multiply 26.97 by 5.

So, 26.97 × 5 ≈ 134.87.

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Max, the Girl Character from BrightChamps

Problem 4

What will be the square root of (728 + 1)?

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The square root is 27.

Explanation

To find the square root, we need to find the sum of (728 + 1). 728 + 1 = 729, and the square root of 729 is 27.

Therefore, the square root of (728 + 1) is 27.

 

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Max, the Girl Character from BrightChamps

Problem 5

Find the perimeter of the rectangle if its length ‘l’ is √728 units and the width ‘w’ is 38 units.

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The perimeter of the rectangle is 129.94 units.

Explanation

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

Perimeter = 2 × (√728 + 38) ≈ 2 × (26.97 + 38) ≈ 2 × 64.97 ≈ 129.94 units.

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FAQ on Square Root of 728

1.What is √728 in its simplest form?

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2.Mention the factors of 728.

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3.Calculate the square of 728.

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4.Is 728 a prime number?

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5.728 is divisible by?

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

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7.How can cultural or local activities in United States support learning Algebra topics such as Square Root of 728?

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8.How do technology and digital tools in United States support learning Algebra and Square Root of 728?

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

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Professor Greenline from BrightChamps

Important Glossaries for the Square Root of 728

  • Square root: A square root is the inverse operation of squaring a number. For example, 4^2 = 16, and the inverse operation is the square root, √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.

 

  • Long division method: A mathematical procedure used to find the square root of numbers, especially non-perfect squares, by breaking down the calculation into simpler steps.

 

  • Approximation method: A technique to estimate the value of a square root by using nearby perfect squares to find a closer value.

 

  • Prime factorization: The process of expressing a number as a product of its prime factors.
Professor Greenline from BrightChamps

About BrightChamps in United States

At BrightChamps, we understand algebra is more than just symbols—it’s a gateway to endless possibilities! Our goal is to empower kids throughout the United States to master key math skills, like today’s topic on the Square Root of 728, with a special emphasis on understanding square roots—in an engaging, fun, and easy-to-grasp manner. Whether your child is calculating how fast a roller coaster zooms through Disney World, keeping track of scores during a Little League game, or budgeting their allowance for the latest gadgets, mastering algebra boosts their confidence to tackle everyday problems. Our hands-on lessons make learning both accessible and exciting. Since kids in the USA learn in diverse ways, we customize our methods to suit each learner’s style. From the lively streets of New York City to the sunny beaches of California, BrightChamps brings math alive, making it meaningful and enjoyable all across America. 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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