124 LearnersLast updated on May 26th, 2025
Square Root of 2035
If a number is multiplied by itself, the result is a square. The inverse operation of squaring is finding the square root. The square root is used in fields like vehicle design, finance, etc. Here, we will discuss the square root of 2035.
What is the Square Root of 2035?
The square root is the inverse of squaring a number. 2035 is not a perfect square. The square root of 2035 is expressed in both radical and exponential form. In radical form, it is expressed as √2035, whereas in exponential form it is expressed as (2035)^(1/2). √2035 ≈ 45.103, 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 2035
The prime factorization method is useful for perfect square numbers. However, for non-perfect square numbers like 2035, the long division method and approximation method are used. Let us now learn these methods:
- Prime factorization method
- Long division method
- Approximation method
Square Root of 2035 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 2035 is broken down into its prime factors.
Step 1: Finding the prime factors of 2035
Breaking it down, we get 5 x 11 x 37
Step 2: Now we found the prime factors of 2035. The second step is to make pairs of those prime factors. Since 2035 is not a perfect square, the digits of the number cannot be grouped into pairs. Therefore, calculating √2035 using prime factorization is not possible.
Square Root of 2035 by Long Division Method
The long division method is particularly used for non-perfect square numbers. In this method, we need to check the closest perfect square number to 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, we need to group the numbers from right to left. In the case of 2035, we group it as 35 and 20.
Step 2: Now we need to find n whose square is closest to 20. We can say n is ‘4’ because 4 x 4 = 16, which is less than 20. The quotient is 4, and after subtracting 16 from 20, the remainder is 4.
Step 3: Bring down 35, making the new dividend 435. Add the old divisor with the same number, 4 + 4, to get 8, which will be our new divisor.
Step 4: The new divisor will be 8n. We need to find the value of n such that 8n x n ≤ 435. Let us consider n as 5, then 85 x 5 = 425.
Step 5: Subtract 425 from 435, the difference is 10, and the quotient is 45.
Step 6: Since the remainder is less than the divisor, we need to add a decimal point. Adding the decimal point allows us to add two zeroes to the remainder. Now the new dividend is 1000.
Step 7: Now we need to find the new divisor that is 901, since 901 x 1 = 901.
Step 8: Subtracting 901 from 1000 gives the result 99.
Step 9: The quotient is 45.1
Step 10: Continue doing these steps until we get two numbers after the decimal point or until the remainder is zero.
So the square root of √2035 ≈ 45.10
Square Root of 2035 by Approximation Method
The approximation method is another method for finding square roots and is an easy method to find the square root of a given number. Let us learn how to find the square root of 2035 using the approximation method.
Step 1: Find the closest perfect squares to √2035. The smallest perfect square less than 2035 is 2025 (with a square root of 45) and the largest perfect square greater than 2035 is 2116 (with a square root of 46). √2035 falls somewhere between 45 and 46.
Step 2: Apply the formula (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square).
Using the formula: (2035 - 2025) ÷ (2116 - 2025) = 10 ÷ 91 ≈ 0.11 Adding this decimal to the integer part, we get 45 + 0.11 = 45.11 So the square root of 2035 is approximately 45.11
Common Mistakes and How to Avoid Them in the Square Root of 2035
Students often make mistakes while finding square roots, such as forgetting about the negative square root or skipping steps in the long division methods. Now, let us look at a few of these common mistakes 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 take only the positive square root as it is used in most real-world applications.
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 symbol properly is another mistake that students make. To resolve this, we need to teach students that simplifying the numbers inside the square root is important before moving to the next step.
For example, √(12+24) ≠ √12 + √24. The correct usage is √(12+24) = √36.
Mistake 3
Not Finding the Correct Value of a Non-Perfect Square
The first step is simplifying the numbers inside the square root to ensure students do not make mistakes while identifying the approximate value.
For example, √50 ≠ 7; the correct answer is √50 ≈ 7.071067.
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 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 an incorrect answer. This may happen in subtracting or elsewhere in the process.
Square Root of 2035 Examples
Problem 1
Can you help Lisa find the area of a square box if its side length is given as √2035?
The area of the square is 2035 square units.
Explanation
The area of the square = side^2.
The side length is given as √2035.
Area of the square = side^2 = √2035 x √2035 = 2035.
Therefore, the area of the square box is 2035 square units.
Problem 2
A square-shaped building measuring 2035 square feet is built; if each of the sides is √2035, what will be the square feet of half of the building?
1017.5 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 2035 by 2 = 1017.5
So half of the building measures 1017.5 square feet.
Problem 3
Calculate √2035 x 5.
225.515
Explanation
The first step is to find the square root of 2035, which is approximately 45.103.
The second step is to multiply 45.103 by 5.
So 45.103 x 5 = 225.515
Problem 4
What will be the square root of (2000 + 35)?
The square root is approximately 45.103.
Explanation
To find the square root, we need to find the sum of (2000 + 35). 2000 + 35 = 2035, and then find √2035 ≈ 45.103.
Therefore, the square root of (2000 + 35) is approximately ±45.103.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √2035 units and the width ‘w’ is 50 units.
The perimeter of the rectangle is approximately 190.206 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√2035 + 50) = 2 × (45.103 + 50) = 2 × 95.103 = 190.206 units.
FAQ on Square Root of 2035
1.What is √2035 in its simplest form?
2.Mention the factors of 2035.
3.Calculate the square of 2035.
4.Is 2035 a prime number?
5.2035 is divisible by?
6.How does learning Algebra help students in Bahrain make better decisions in daily life?
7.How can cultural or local activities in Bahrain support learning Algebra topics such as Square Root of 2035?
8.How do technology and digital tools in Bahrain support learning Algebra and Square Root of 2035?
9.Does learning Algebra support future career opportunities for students in Bahrain?
Important Glossaries for the Square Root of 2035
- Square root: A square root is a value that, when multiplied by itself, gives the original number. Example: 4^2 = 16, so √16 = 4.
- Irrational number: An irrational number is a number that cannot be written as a simple fraction, which means it cannot be expressed as p/q, where p and q are integers, and q is not zero.
- Radical: A radical is a symbol (√) used to denote the square root or nth root of a number.
- Perfect square: A perfect square is a number that is the square of an integer. For example, 1, 4, 9, 16, etc., are perfect squares.
- Decimal: A decimal is a number that includes a whole number and a fractional part separated by a decimal point, for example: 7.86, 8.65, and 9.42.
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About BrightChamps in Bahrain
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.
