125 LearnersLast updated on May 26th, 2025
Square Root of 2034
If a number is multiplied by itself, the result is a square. The inverse operation of squaring a number is finding its square root. Square roots have applications in various fields like vehicle design, finance, and more. Here, we will discuss the square root of 2034.
What is the Square Root of 2034?
The square root is the inverse operation of squaring a number. 2034 is not a perfect square. The square root of 2034 can be expressed in both radical and exponential form. In radical form, it is expressed as √2034, whereas in exponential form, it is written as (2034)^(1/2). The approximate value of √2034 is 45.092, 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 2034
The prime factorization method is suitable for perfect square numbers, but for non-perfect squares like 2034, other methods such as the long division method and approximation method are used. Let us now learn the following methods:
- Long division method
- Approximation method
Square Root of 2034 by Long Division Method
The long division method is effective for finding the square root of non-perfect square numbers. Here are the steps to find the square root of 2034 using the long division method:
Step 1: Group the numbers from right to left. For 2034, group it as 20 and 34.
Step 2: Find a number whose square is less than or equal to 20. The number is 4, since 4 × 4 = 16. Subtract 16 from 20 to get a remainder of 4.
Step 3: Bring down the next pair of digits, 34, making the new dividend 434.
Step 4: Double the divisor (4) to get 8, which forms the beginning of the new divisor.
Step 5: Find digit n such that 8n × n is less than or equal to 434. Here, n is 5, since 85 × 5 = 425.
Step 6: Subtract 425 from 434 to get a remainder of 9.
Step 7: Since the dividend (9) is less than the divisor (85), add a decimal point and bring down two zeros, making the new dividend 900.
Step 8: Continue the process to find more digits after the decimal point until the desired accuracy is achieved.
The square root of 2034 is approximately 45.092.
Square Root of 2034 by Approximation Method
The approximation method is a straightforward way to find the square root of a number. Here’s how to find the square root of 2034 using approximation:
Step 1: Identify the perfect squares closest to 2034. The perfect square less than 2034 is 2025, and the one greater is 2116. So, √2034 falls between √2025 and √2116, i.e., between 45 and 46.
Step 2: Use the formula: (Given number - smaller perfect square) ÷ (larger perfect square - smaller perfect square) Calculating: (2034 - 2025) ÷ (2116 - 2025) = 9 ÷ 91 ≈ 0.099
Step 3: Add this value to the smaller root: 45 + 0.099 = 45.099 Therefore, the approximate square root of 2034 is 45.099.
Common Mistakes and How to Avoid Them in the Square Root of 2034
Students often make mistakes when calculating square roots, such as forgetting about the negative square root or skipping steps in the long division method. Here are some common mistakes and how to avoid them:
Mistake 1
Forgetting about the negative square root
It is important to remember that a number has both positive and negative square roots. However, in most practical applications, we consider only the positive square root.
For example, √50 = ±7.07, but usually, only 7.07 is used.
Mistake 2
Not adding the square root symbol in proper places
Incorrect use of the square root symbol is a common mistake. It's crucial to simplify numbers inside the square root before proceeding.
For example, √(12 + 24) should be simplified to √36, not √12 + √24.
Mistake 3
Not finding the correct value of a non-perfect square
Students should simplify numbers inside the square root to avoid errors in approximating the value.
For example, √50 should be approximately 7.071067, not simply 7.
Mistake 4
Confusing the square root symbol with the cube root
Students should understand the difference between square roots and cube roots.
For example, √50 and ∛50 are different and should not be confused.
Mistake 5
Making mistakes in long division
Finding a square root using the long division method involves several steps. Students might skip a step accidentally, leading to incorrect results. Careful attention to each step is necessary to avoid errors.
Square Root of 2034 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √2034?
The area of the square is 4130.328 square units.
Explanation
The area of a square = side².
The side length is given as √2034.
Area = side² = √2034 × √2034 ≈ 45.092 × 45.092 = 2034.328
Therefore, the area of the square box is approximately 2034.328 square units.
Problem 2
A square-shaped building measuring 2034 square feet is built; if each of the sides is √2034, what will be the square feet of half of the building?
1017 square feet
Explanation
To find half of the area of the building, simply divide the given area by 2.
Dividing 2034 by 2 = 1017
So, half of the building measures 1017 square feet.
Problem 3
Calculate √2034 × 3.
135.276
Explanation
First, find the square root of 2034, which is approximately 45.092.
Multiply 45.092 by 3.
So, 45.092 × 3 ≈ 135.276.
Problem 4
What will be the square root of (2034 + 16)?
The square root is approximately 46.
Explanation
To find the square root, first find the sum of (2034 + 16). 2034 + 16 = 2050, and then find √2050, which is approximately 45.276.
Therefore, the approximate square root of (2034 + 16) is 45.276.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √2034 units and the width ‘w’ is 50 units.
The perimeter of the rectangle is approximately 190.184 units.
Explanation
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√2034 + 50) = 2 × (45.092 + 50) = 2 × 95.092 = 190.184 units.
FAQ on Square Root of 2034
1.What is √2034 in its simplest form?
2.Mention the factors of 2034.
3.Calculate the square of 2034.
4.Is 2034 a prime number?
5.2034 is divisible by?
6.How does learning Algebra help students in Thailand make better decisions in daily life?
7.How can cultural or local activities in Thailand support learning Algebra topics such as Square Root of 2034?
8.How do technology and digital tools in Thailand support learning Algebra and Square Root of 2034?
9.Does learning Algebra support future career opportunities for students in Thailand?
Important Glossaries for the Square Root of 2034
- Square root: The square root of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 16 is 4 because 4 × 4 = 16.
- Irrational number: An irrational number is a number that cannot be expressed as a simple fraction, with non-repeating and non-terminating decimal expansions.
- Decimal: A number that consists of a whole number and a fractional part separated by a decimal point, like 7.86 or 45.092.
- Perfect square: A number that is the square of an integer. For example, 16 is a perfect square because it is 4 squared.
- Long division method: A technique used to find the square root of a number by dividing the number into groups of two digits, starting from the decimal point or from the right for whole numbers.
Explore More algebra
About BrightChamps in Thailand
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.
