127 LearnersLast updated on May 26th, 2025
Square Root of 3400
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 3400.
What is the Square Root of 3400?
The square root is the inverse of the square of the number. 3400 is not a perfect square. The square root of 3400 is expressed in both radical and exponential form. In the radical form, it is expressed as √3400, whereas (3400)^(1/2) is its exponential form. √3400 ≈ 58.3095, 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 3400
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 3400 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 3400 is broken down into its prime factors.
Step 1: Finding the prime factors of 3400 Breaking it down, we get 2 x 2 x 2 x 5 x 5 x 17: 2^3 x 5^2 x 17
Step 2: Now we found the prime factors of 3400. The second step is to make pairs of those prime factors. Since 3400 is not a perfect square, the digits of the number can’t be grouped into pairs. Therefore, calculating 3400 using prime factorization is limited.
Square Root of 3400 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 3400, we need to group it as 00 and 34.
Step 2: Now, we need to find n whose square is less than or equal to 34. We can say n is '5' because 5 x 5 = 25, which is less than 34. The quotient is 5, and after subtracting 25 from 34, the remainder is 9.
Step 3: Bring down the next pair of digits, which is 00, to make the new dividend 900.
Step 4: Add the old divisor to itself, 5 + 5, to get 10, which becomes our new divisor.
Step 5: Find a digit 'd' such that (10d) x d is less than or equal to 900. In this case, d is 8, since 108 x 8 = 864.
Step 6: Subtract 864 from 900 to get 36 as the remainder, and the quotient is now 58.
Step 7: Since the dividend is less than the divisor, we add a decimal point and continue the division. Add two zeroes to the dividend, making it 3600.
Step 8: The new divisor becomes 580. Finding the suitable digit gives us the quotient 58.3. Continue this process to find more decimal places as needed. So the square root of √3400 is approximately 58.3095.
Square Root of 3400 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 3400 using the approximation method.
Step 1: Find the closest perfect squares around 3400. The closest perfect squares are 3364 (58^2) and 3481 (59^2). √3400 falls between 58 and 59.
Step 2: Apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square) Using the formula: (3400 - 3364) / (3481 - 3364) ≈ 0.365 The approximation step gives us the decimal value. Adding this to the base integer, 58 + 0.365 = 58.365, so the square root of 3400 is approximately 58.365.
Common Mistakes and How to Avoid Them in the Square Root of 3400
Students do make mistakes while finding the square root, such as forgetting about the negative square root or skipping steps in the long division method. Let's look at a few 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 in most real-world contexts.
For example: √50 = 7.07, but 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. We need to teach children that simplifying the numbers inside the square root is important before moving to the next step.
For example, √(12 + 24) = √36 is correct, not √12 + √24.
Mistake 3
Not finding the correct value of a non-perfect square
The first step 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 incorrect; 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 to avoid confusion.
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. This may happen while subtracting or elsewhere.
Square Root of 3400 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √3400?
The area of the square is approximately 3400 square units.
Explanation
The area of the square = side^2.
The side length is given as √3400.
Area of the square = side^2 = √3400 x √3400 = 3400
Therefore, the area of the square box is approximately 3400 square units.
Problem 2
A square-shaped building measuring 3400 square feet is built; if each of the sides is √3400, what will be the square feet of half of the building?
1700 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 3400 by 2 = 1700
So half of the building measures 1700 square feet.
Problem 3
Calculate √3400 x 5.
Approximately 291.55
Explanation
The first step is to find the square root of 3400, which is approximately 58.31.
The second step is to multiply 58.31 by 5.
So 58.31 x 5 ≈ 291.55
Problem 4
What will be the square root of (3400 + 100)?
The square root is 60
Explanation
To find the square root, we need to find the sum of (3400 + 100).
3400 + 100 = 3500, and √3500 ≈ 59.16.
Therefore, the square root of (3400 + 100) is approximately 59.16.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √3400 units and the width ‘w’ is 50 units.
We find the perimeter of the rectangle as approximately 216.62 units.
Explanation
Perimeter of the rectangle = 2 × (length + width) Perimeter = 2 × (√3400 + 50) ≈ 2 × (58.31 + 50) ≈ 2 × 108.31 ≈ 216.62 units.
FAQ on Square Root of 3400
1.What is √3400 in its simplest form?
2.Mention the factors of 3400.
3.Calculate the square of 3400.
4.Is 3400 a prime number?
5.3400 is divisible by?
6.How does learning Algebra help students in Qatar make better decisions in daily life?
7.How can cultural or local activities in Qatar support learning Algebra topics such as Square Root of 3400?
8.How do technology and digital tools in Qatar support learning Algebra and Square Root of 3400?
9.Does learning Algebra support future career opportunities for students in Qatar?
Important Glossaries for the Square Root of 3400
- Square root: A square root is the number that, when multiplied by itself, gives the original number. Example: The square root of 25 is 5 because 5 x 5 = 25.
- Irrational number: An irrational number is a number that cannot be expressed as a simple fraction. Its decimal form is non-repeating and non-terminating.
- Perfect square: A perfect square is an integer that is the square of an integer. For example, 9 is a perfect square because it is 3 x 3.
- Prime factorization: Prime factorization is the process of expressing a number as the product of its prime numbers. For example, the prime factorization of 18 is 2 x 3 x 3.
- Long division method: The long division method is a technique to find the square root of a number by dividing and averaging iteratively.
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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.
