122 LearnersLast updated on May 26th, 2025
Square Root of 3479
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.
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.
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
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.
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.
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.
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
Forgetting about the negative square root
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.
Mistake 2
Not adding the square root symbol in proper places
Not using the square root properly is another mistake that children make. To resolve this, we need to teach children that simplifying the numbers inside the square root is important and then move on to the second step.
For example: √(12 + 24) = √12 + √24 is a wrong method. The right way is √(12 + 24) = √36 = 6.
Mistake 3
Not finding the correct value of a non-perfect square
The first step that needs to be taught to children is to simplify the numbers inside the square root. This is important so that students do not make mistakes while identifying the approximate value.
For example: √50 = 7 is wrong, the correct answer is √50 ≈ 7.071.
Mistake 4
Confusing the square root symbol with the cube root
Students need to be taught the difference between cube root and square root constantly as this will help them avoid mistakes.
For example: √50 and ∛50 are different.
Mistake 5
Making mistakes in long division
Finding a square root using the long division method involves many steps. Due to this, many students might skip a step accidentally, which results in a wrong answer at the end. This may either happen in subtracting or elsewhere.
Square Root of 3479 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √3479?
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.
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?
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.
Problem 3
Calculate √3479 × 5.
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.
Problem 4
What will be the square root of (1379 + 2100)?
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.
Problem 5
Find the perimeter of a rectangle if its length 'l' is √3479 units and the width 'w' is 20 units.
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.
FAQ on Square Root of 3479
1.What is √3479 in its simplest form?
2.Mention the factors of 3479.
3.Calculate the square of 3479.
4.Is 3479 a prime number?
5.3479 is divisible by?
6.How does learning Algebra help students in Oman make better decisions in daily life?
7.How can cultural or local activities in Oman support learning Algebra topics such as Square Root of 3479?
8.How do technology and digital tools in Oman support learning Algebra and Square Root of 3479?
9.Does learning Algebra support future career opportunities for students in Oman?
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.
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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.
Fun Fact
: He loves to play the quiz with kids through algebra to make kids love it.
