118 LearnersLast updated on May 26th, 2025
Square Root of 2012
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 2012.
What is the Square Root of 2012?
The square root is the inverse of the square of the number. 2012 is not a perfect square. The square root of 2012 is expressed in both radical and exponential form. In the radical form, it is expressed as √2012, whereas (2012)^(1/2) in the exponential form. √2012 ≈ 44.833, 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 2012
The prime factorization method is used for perfect square numbers. However, the prime factorization method is not used for non-perfect square numbers where 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 2012 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 2012 is broken down into its prime factors.
Step 1: Finding the prime factors of 2012
Breaking it down, we get 2 x 2 x 503: 2² x 503¹
Step 2: Now we found out the prime factors of 2012. The second step is to make pairs of those prime factors. Since 2012 is not a perfect square, therefore the digits of the number can’t be grouped in pairs. Therefore, calculating 2012 using prime factorization is impossible.
Square Root of 2012 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 2012, we need to group it as 12 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 4² = 16, which is less than 20. The quotient is 4, and after subtracting 16 from 20, the remainder is 4.
Step 3: Now let us bring down 12, which is the new dividend. Add the old divisor with the same number: 4 + 4, we get 8, which will be our new divisor.
Step 4: The new divisor will be the sum of the dividend and quotient. Now we get 8n as the new divisor, we need to find the value of n.
Step 5: The next step is finding 8n × n ≤ 412. Let us consider n as 5, now 85 x 5 = 425, which is too high, so we consider n as 4. We have 84 x 4 = 336.
Step 6: Subtract 336 from 412, the difference is 76, and the quotient becomes 44.
Step 7: Since the dividend is less than the divisor, we need to add a decimal point. Adding the decimal point allows us to add two zeroes to the dividend. Now the new dividend is 7600.
Step 8: Now we need to find n for the new divisor 888n ≤ 7600. Let's consider n as 8, then 888 x 8 = 7104.
Step 9: Subtracting 7104 from 7600, we get the result 496.
Step 10: Now the quotient is 44.8
Step 11: Continue doing these steps until we get two numbers after the decimal point. If no decimal values appear, continue until the remainder is zero.
So the square root of √2012 is approximately 44.83.
Square Root of 2012 by Approximation Method
The approximation method is another method for finding 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 2012 using the approximation method.
Step 1: Now we have to find the closest perfect squares of √2012. The smallest perfect square less than 2012 is 2025, and the largest perfect square greater than 2012 is 1936. √2012 falls somewhere between 44 and 45.
Step 2: Now we need to apply the formula that is (Given number - smallest perfect square) / (Largest perfect square - smallest perfect square). Going by the formula (2012 - 1936) ÷ (2025 - 1936) = 76/89 ≈ 0.85
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 44 + 0.85 ≈ 44.85, so the square root of 2012 is approximately 44.85.
Common Mistakes and How to Avoid Them in the Square Root of 2012
Students do make mistakes while finding the square root, such as forgetting about the negative square root, skipping long division methods, etc. Now let us look at a few of those 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 does have both positive and negative square roots. However, we will be taking 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 properly is another mistake that children make. To resolve this, we need to teach children that simplifying the numbers inside the square root is important and then move on to the second step.
For example: √(12+24) = √12 + √24 is a wrong method of using roots. The right way of using roots is √(12+24) = √36.
Mistake 3
Not finding the correct value of a non-perfect square
The first step that needs to be taught to children 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 wrong, 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 constantly as this will help them keep away from 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, which results in a wrong answer at the end of the calculation. This may either happen in subtracting or elsewhere.
Square Root of 2012 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √1012?
The area of the square is 1012 square units.
Explanation
The area of the square = side².
The side length is given as √1012.
Area of the square = side² = √1012 x √1012 = 31.81 × 31.81 = 1012
Therefore, the area of the square box is 1012 square units.
Problem 2
A square-shaped building measuring 2012 square feet is built; if each of the sides is √2012, what will be the square feet of half of the building?
1006 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 2012 by 2 = we get 1006
So half of the building measures 1006 square feet.
Problem 3
Calculate √2012 × 5.
224.165
Explanation
The first step is to find the square root of 2012, which is approximately 44.833, the second step is to multiply 44.833 with 5.
So 44.833 × 5 = 224.165.
Problem 4
What will be the square root of (1012 + 1000)?
The square root is approximately 44.72
Explanation
To find the square root, we need to find the sum of (1012 + 1000). 1012 + 1000 = 2012, and then √2012 ≈ 44.72.
Therefore, the square root of (1012 + 1000) is approximately ±44.72.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √1012 units and the width ‘w’ is 38 units.
We find the perimeter of the rectangle as 139.62 units.
Explanation
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√1012 + 38) = 2 × (31.81 + 38) = 2 × 69.81 = 139.62 units.
FAQ on Square Root of 2012
1.What is √2012 in its simplest form?
2.Mention the factors of 2012.
3.Calculate the square of 2012.
4.Is 2012 a prime number?
5.2012 is divisible by?
6.How does learning Algebra help students in India make better decisions in daily life?
7.How can cultural or local activities in India support learning Algebra topics such as Square Root of 2012?
8.How do technology and digital tools in India support learning Algebra and Square Root of 2012?
9.Does learning Algebra support future career opportunities for students in India?
Important Glossaries for the Square Root of 2012
- Square root: A square root is the inverse of a square. Example: 4² = 16 and the inverse of the square is the square root, that is √16 = 4.
- Irrational number: An irrational number is a number that cannot be written in the form of p/q, q is not equal to zero and p and q are integers.
- Long division method: A method used to find the square roots of non-perfect squares by dividing and averaging.
- Approximation method: A method used to find a close estimate of a square root by comparing with nearby perfect squares.
- Perfect square: A number that is the square of an integer. Example: 144, because 12 x 12 = 144.
Explore More algebra
About BrightChamps in India
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.
