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Last updated on May 26th, 2025

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Square Root of 3479

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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 3479.

Square Root of 3479 for Omani Students
Professor Greenline from BrightChamps

What is the Square Root of 3479?

The square root is the inverse of the square of the number. 3479 is not a perfect square. The square root of 3479 is expressed in both radical and exponential form. In the radical form, it is expressed as √3479, whereas (3479)^(1/2) in the exponential form. √3479 ≈ 59.0, 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 3479

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 3479 by Prime Factorization Method

The product of prime factors is the prime factorization of a number. Now let us look at how 3479 is broken down into its prime factors.

 

Step 1: Finding the prime factors of 3479. Breaking it down, we get 3479 = 59 × 59.

 

Step 2: Now we found out the prime factors of 3479. The second step is to make pairs of those prime factors. Since 3479 is not a perfect square, therefore the digits of the number can’t be grouped in pairs without a remainder. Therefore, calculating 3479 using prime factorization is impossible without approximation.

Professor Greenline from BrightChamps

Square Root of 3479 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 3479, we need to group it as 79 and 34.

 

Step 2: Now we need to find n whose square is less than or equal to 34. We find n as 5, because 5 × 5 = 25 is less than 34. Now the quotient is 5, and after subtracting 25 from 34, the remainder is 9.

 

Step 3: Now let us bring down 79, making the new dividend 979. Add the old divisor 5 to itself to get 10, which will be our new divisor's starting point.

 

Step 4: Find a digit x such that 10x × x ≤ 979. Trying x = 9, we get 109 × 9 = 981, which is too large, so we try x = 8.

 

Step 5: 108 × 8 = 864, which fits within 979. Subtract to get a remainder of 115.

 

Step 6: 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 11500.

 

Step 7: Find a new digit y such that 1080y × y ≤ 11500. Trying y = 6, we find 10806 × 6 = 64836, which is too large, so we try y = 5.

 

Step 8: 10805 × 5 = 54025. Subtracting gives a remainder.

 

Step 9: Continue these steps until we have the desired decimal places. So the square root of √3479 is approximately 59.0.

Professor Greenline from BrightChamps

Square Root of 3479 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 3479 using the approximation method.

 

Step 1: Find the closest perfect squares of √3479. The smallest perfect square less than 3479 is 3364 (58²) and the largest perfect square greater than 3479 is 3481 (59²). √3479 falls between 58 and 59.

 

Step 2: Now we need to apply the formula: (Given number - smallest perfect square) ÷ (Greater perfect square - smallest perfect square). Using the formula (3479 - 3364) ÷ (3481 - 3364) = 115 ÷ 117 ≈ 0.98. 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 58 + 0.98 = 58.98, so the square root of 3479 is approximately 59.0.

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Common Mistakes and How to Avoid Them in the Square Root of 3479

Students do make mistakes while finding the square root, such as forgetting about the negative square root or skipping long division methods. 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 3479 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 √3479?

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The area of the square is approximately 3479 square units.

Explanation

The area of a square = side².

The side length is given as √3479.

Area of the square = side² = √3479 × √3479 = 3479.

Therefore, the area of the square box is approximately 3479 square units.

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Max, the Girl Character from BrightChamps

Problem 2

A square-shaped building measuring 3479 square feet is built; if each of the sides is √3479, what will be the square feet of half of the building?

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1739.5 square feet

Explanation

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

Dividing 3479 by 2, we get 1739.5.

So, half of the building measures 1739.5 square feet.

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Max, the Girl Character from BrightChamps

Problem 3

Calculate √3479 × 5.

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295.0

Explanation

The first step is to find the square root of 3479, which is approximately 59.0. The second step is to multiply 59.0 by 5. So, 59.0 × 5 = 295.0.

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Max, the Girl Character from BrightChamps

Problem 4

What will be the square root of (1379 + 2100)?

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The square root is 60.

Explanation

To find the square root, we need to find the sum of (1379 + 2100).

1379 + 2100 = 3479, and then √3479 ≈ 59.0.

Therefore, the square root of (1379 + 2100) is approximately 59.0.

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Max, the Girl Character from BrightChamps

Problem 5

Find the perimeter of a rectangle if its length 'l' is √3479 units and the width 'w' is 20 units.

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

The perimeter of the rectangle is approximately 158 units.

Explanation

Perimeter of the rectangle = 2 × (length + width). Perimeter = 2 × (√3479 + 20) = 2 × (59.0 + 20) = 2 × 79.0 = 158 units.

Max from BrightChamps Praising Clear Math Explanations
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FAQ on Square Root of 3479

1.What is √3479 in its simplest form?

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2.Mention the factors of 3479.

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3.Calculate the square of 3479.

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4.Is 3479 a prime number?

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5.3479 is divisible by?

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

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7.How can cultural or local activities in Oman support learning Algebra topics such as Square Root of 3479?

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8.How do technology and digital tools in Oman support learning Algebra and Square Root of 3479?

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

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Professor Greenline from BrightChamps

Important Glossaries for the Square Root of 3479

  • Square root: A square root is the inverse of a square. Example: 4² = 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, q is not equal to zero, and p and q are integers.

 

  • Long division method: A method used to find the square root of non-perfect squares by dividing the number into groups and performing division and subtraction iteratively.

 

  • Approximation method: A method used to estimate the square root of a number by finding its closest perfect squares and interpolating between them.

 

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

About BrightChamps in Oman

At BrightChamps, we understand algebra as more than symbols—it’s a key to unlocking many opportunities! Our mission is to help children across Oman gain important math skills, focusing today on the Square Root of 3479 with special attention to square roots—in an engaging, lively, and easy-to-follow manner. Whether your child is measuring how fast a roller coaster moves at Oman’s Dreamland Aqua Park, tracking local football scores, or managing their allowance for the latest gadgets, mastering algebra gives them confidence for everyday tasks. Our hands-on lessons make learning simple and fun. Because children in Oman learn differently, we adapt lessons to fit each learner’s style. From Muscat’s vibrant city life to beautiful natural landscapes, BrightChamps brings math to life, making it exciting throughout Oman. Let’s make square roots a joyful part of every child’s math journey!
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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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