124 LearnersLast updated on May 26th, 2025
Square Root of 339
If a number is multiplied by itself, the result is a square. The inverse operation of finding a square is called finding the square root. The square root is used in various fields, including vehicle design, finance, etc. Here, we will discuss the square root of 339.
What is the Square Root of 339?
The square root is the inverse operation of squaring a number. 339 is not a perfect square. The square root of 339 is expressed in both radical and exponential form. In radical form, it is expressed as √339, whereas in exponential form it is expressed as (339)^(1/2). √339 ≈ 18.412, 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 339
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
Square Root of 339 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 339 is broken down into its prime factors:
Step 1: Finding the prime factors of 339 Breaking it down, we get 3 x 113
Step 2: Now we have found the prime factors of 339. Since 339 is not a perfect square, the digits of the number can’t be grouped into pairs.
Therefore, calculating √339 using prime factorization is not possible.
Square Root of 339 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 339, we need to group it as 39 and 3.
Step 2: Now we need to find n whose square is less than or equal to 3. We can say n is ‘1’ because 1 x 1 is less than or equal to 3. Now the quotient is 1; after subtracting 1 from 3, the remainder is 2.
Step 3: Now let us bring down 39, which is the new dividend. Add the old divisor with the same number 1 + 1 to get 2, which will be our new divisor.
Step 4: The new divisor will be the sum of the dividend and quotient. Now we get 2n as the new divisor, and we need to find the value of n.
Step 5: The next step is finding 2n × n ≤ 239. Let us consider n as 8, now 28 x 8 = 224
Step 6: Subtract 224 from 239, and the difference is 15. The quotient is 18.
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 1500.
Step 8: Now we need to find the new divisor. Considering 286, because 286 x 6 = 1716 is too large, we try 285 x 5 = 1425.
Step 9: Subtracting 1425 from 1500 gives 75.
Step 10: Now the quotient is 18.4
Step 11: Continue doing these steps until we get two numbers after the decimal point. If there are no decimal values, continue until the remainder is zero.
So the square root of √339 is approximately 18.41.
Square Root of 339 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 339 using the approximation method.
Step 1: We need to find the closest perfect square to √339.
The smallest perfect square less than 339 is 324, and the largest perfect square more than 339 is 361. √339 falls somewhere between 18 and 19.
Step 2: Now we need to apply the formula: (Given number - smallest perfect square) ÷ (Greater perfect square - smallest perfect square)
Using the formula (339 - 324) ÷ (361 - 324) = 15 ÷ 37 = 0.405 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 18 + 0.405 ≈ 18.41.
So the square root of 339 is approximately 18.41.
Common Mistakes and How to Avoid Them in the Square Root of 339
Students often make mistakes while finding the square root, such as forgetting about the negative square root, skipping long division methods, etc. 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 has both positive and negative square roots. However, we usually consider 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 the wrong method of using roots. The right way is √(12+24) = √36.
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 the cube root and the 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, resulting in a wrong answer at the end of the sum. This may either happen in subtracting or elsewhere.
Square root of 339 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √339?
The area of the square is 339 square units.
Explanation
The area of the square = side².
The side length is given as √339.
Area of the square = side² = √339 x √339 = 339.
Therefore, the area of the square box is 339 square units.
Problem 2
A square-shaped building measuring 339 square feet is built; if each of the sides is √339, what will be the square feet of half of the building?
169.5 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 339 by 2 = we get 169.5
So half of the building measures 169.5 square feet.
Problem 3
Calculate √339 x 5.
Approximately 92.06
Explanation
The first step is to find the square root of 339, which is approximately 18.41.
The second step is to multiply 18.41 by 5.
So, 18.41 x 5 ≈ 92.06.
Problem 4
What will be the square root of (339 + 5)?
The square root is approximately 18.52.
Explanation
To find the square root, we need to find the sum of (339 + 5). 339 + 5 = 344, and then √344 ≈ 18.52.
Therefore, the square root of (339 + 5) is approximately ±18.52.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √339 units and the width ‘w’ is 20 units.
We find the perimeter of the rectangle is approximately 76.82 units.
Explanation
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√339 + 20) ≈ 2 × (18.41 + 20) ≈ 2 × 38.41 ≈ 76.82 units.
FAQ on Square Root of 339
1.What is √339 in its simplest form?
2.Mention the factors of 339.
3.Calculate the square of 339.
4.Is 339 a prime number?
5.339 is divisible by?
6.How does learning Algebra help students in Saudi Arabia make better decisions in daily life?
7.How can cultural or local activities in Saudi Arabia support learning Algebra topics such as Square Root of 339?
8.How do technology and digital tools in Saudi Arabia support learning Algebra and Square Root of 339?
9.Does learning Algebra support future career opportunities for students in Saudi Arabia?
Important Glossaries for the Square Root of 339
- Square root: A square root is the inverse of a square. Example: 4² = 16, and the inverse of the square is the square root, which 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.
- Perfect square: A perfect square is a number that is the square of an integer. For example, 16 and 25 are perfect squares.
- Radical: A radical is an expression that includes a square root, cube root, etc. For example, √16 and ∛27 are radicals.
- Long division method: A method used for finding the square roots of non-perfect squares through a step-by-step division process.
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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
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