126 LearnersLast updated on May 26th, 2025
Square Root of 2036
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 fields like vehicle design, finance, etc. Here, we will discuss the square root of 2036.
What is the Square Root of 2036?
The square root is the inverse of the square of the number. 2036 is not a perfect square. The square root of 2036 is expressed in both radical and exponential forms. In the radical form, it is expressed as √2036, whereas (2036)^(1/2) in the exponential form. √2036 ≈ 45.116, 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 2036
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 2036 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 2036 is broken down into its prime factors.
Step 1: Finding the prime factors of 2036
Breaking it down, we get 2 x 2 x 509: 2^2 x 509
Step 2: Now we found out the prime factors of 2036. The second step is to make pairs of those prime factors. Since 2036 is not a perfect square, therefore the digits of the number can’t be grouped in pairs. Thus, calculating 2036 using prime factorization is challenging.
Square Root of 2036 by Long Division Method
The long division method is particularly used for non-perfect square numbers. In this method, we check the closest perfect square number for the given number. Let's 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 2036, we group it as 36 and 20.
Step 2: Now we need to find n whose square is less than or equal to 20. We can say n is '4' because 4 x 4 = 16 is less than 20. The quotient is 4, and the remainder is 4 after subtracting 16 from 20.
Step 3: Now let us bring down 36, which is the new dividend. Add the old divisor with the quotient, 4 + 4, to get 8, which will be our new divisor.
Step 4: Finding 8n × n ≤ 436, let us consider n as 5, now 8 x 5 x 5 = 400
Step 5: Subtract 400 from 436, the difference is 36, and the quotient is 45
Step 6: Since the dividend is less than the divisor, we add a decimal point. Adding the decimal point allows us to add two zeroes to the dividend. Now the new dividend is 3600.
Step 7: We need to find the new divisor that is 901 because 901 x 4 = 3604
Step 8: Subtracting 3604 from 3600 gives us the result -4.
Step 9: The quotient is approximately 45.116
Step 10: Continue doing these steps until we get two numbers after the decimal point, or continue till the remainder is zero.
So the square root of √2036 ≈ 45.116
Square Root of 2036 by Approximation Method
The approximation method is another way to find the square roots; it is an easy method for finding square roots of numbers. Now let's learn how to find the square root of 2036 using the approximation method.
Step 1: Now we have to find the closest perfect square of √2036 The smallest perfect square near 2036 is 2025, and the largest perfect square beyond it is 2116. √2036 falls somewhere between 45 and 46.
Step 2: Now we need to apply the formula that is (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square) Going by the formula (2036 - 2025) ÷ (2116 - 2025) = 11/91 ≈ 0.121
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 45 + 0.121 ≈ 45.121
Common Mistakes and How to Avoid Them in the Square Root of 2036
Students do make mistakes while finding the square root, like forgetting about the negative square root, skipping long division methods, etc. Let's look at a few of these mistakes 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 often 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 square root symbol in proper places
Not using the square root symbol properly is another mistake. It's important to simplify numbers inside the square root before moving on.
For example: √(12+24) = √12 + √24 is incorrect. The correct way is √(12+24) = √36.
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 crucial so students do not err in 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 learn 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, so students might skip a step accidentally, resulting in a wrong answer. This can occur during subtraction or elsewhere.
Square Root of 2036 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √2036?
The area of the square is approximately 4145.536 square units.
Explanation
The area of the square = side^2.
The side length is given as √2036.
Area of the square = side^2 = √2036 × √2036 ≈ 45.116 × 45.116 ≈ 2036
Therefore, the area of the square box is approximately 4145.536 square units.
Problem 2
A square-shaped building measuring 2036 square feet is built; if each of the sides is √2036, what will be the square feet of half of the building?
1018 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 2036 by 2, we get 1018.
So half of the building measures 1018 square feet.
Problem 3
Calculate √2036 × 5.
225.58
Explanation
The first step is to find the square root of 2036, which is approximately 45.116.
The second step is to multiply 45.116 by 5.
So 45.116 × 5 ≈ 225.58.
Problem 4
What will be the square root of (2016 + 20)?
The square root is 46.
Explanation
To find the square root, we need to find the sum of (2016 + 20). 2016 + 20 = 2036, and then √2036 ≈ 45.116.
Therefore, the square root of (2016 + 20) is approximately ±45.116.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √2036 units and the width ‘w’ is 38 units.
The perimeter of the rectangle is approximately 166.232 units.
Explanation
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√2036 + 38) ≈ 2 × (45.116 + 38) ≈ 2 × 83.116 = 166.232 units.
FAQ on Square Root of 2036
1.What is √2036 in its simplest form?
2.Mention the factors of 2036.
3.Calculate the square of 2036.
4.Is 2036 a prime number?
5.2036 is divisible by?
6.How does learning Algebra help students in United States make better decisions in daily life?
7.How can cultural or local activities in United States support learning Algebra topics such as Square Root of 2036?
8.How do technology and digital tools in United States support learning Algebra and Square Root of 2036?
9.Does learning Algebra support future career opportunities for students in United States?
Important Glossaries for the Square Root of 2036
- Square root: A square root is the inverse of a square. Example: 4^2 = 16, and the inverse of the square is the square root, which is √16 = 4.
- Irrational number: An irrational number cannot be written in the form of p/q, where q is not equal to zero, and p and q are integers.
- Principal square root: A number has both positive and negative square roots, but the positive square root, known as the principal square root, is more commonly used due to its real-world applications.
- Long division method: A step-by-step method used to find the square root of a number, especially when it is not a perfect square.
- Approximation method: A technique used to estimate the square root of a number by comparing it to nearby perfect squares.
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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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