Last updated on May 26th, 2025
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.
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.
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:
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.
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
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
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.
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.
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.
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
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.
Calculate √2036 × 5.
225.58
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.
What will be the square root of (2016 + 20)?
The square root is 46.
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.
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.
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√2036 + 38) ≈ 2 × (45.116 + 38) ≈ 2 × 83.116 = 166.232 units.
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.
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