125 LearnersLast updated on May 26th, 2025
Square Root of 2001
If a number is multiplied by itself, the result is a square. The inverse of the square is a square root. The square root is used in various fields such as vehicle design and finance. Here, we will discuss the square root of 2001.
What is the Square Root of 2001?
The square root is the inverse of the square of the number. 2001 is not a perfect square. The square root of 2001 is expressed in both radical and exponential form. In radical form, it is expressed as √2001, whereas in exponential form, it is (2001)^(1/2). The square root of 2001 is approximately 44.72136, 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 2001
The prime factorization method is used for perfect square numbers. However, for non-perfect square numbers, the prime factorization method is not used; instead, the long-division method and approximation method are employed. Let us now learn the following methods:
- Prime factorization method
- Long division method
- Approximation method
Square Root of 2001 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 2001 is broken down into its prime factors.
Step 1: Finding the prime factors of 2001
Breaking it down, we get 3 x 23 x 29.
Step 2: Now we found out the prime factors of 2001. Since 2001 is not a perfect square, the digits of the number can’t be grouped in pairs. Therefore, calculating 2001 using prime factorization does not yield an exact square root.
Square Root of 2001 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 2001, we need to group it as 01 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, which is less than 20. Now the quotient is 4 after subtracting 20-16, the remainder is 4.
Step 3: Bring down 01, making the new dividend 401. Add the old divisor (4) to the quotient (4), giving us 8 as the new divisor.
Step 4: The new divisor should be 8n, and we need to find n such that 8n x n ≤ 401. Let n be 5, then 85 x 5 = 425, which is greater than 401, so we need to try n = 4, giving us 84 x 4 = 336.
Step 5: Subtract 336 from 401, the difference is 65, and we add a decimal point to the quotient to continue.
Step 6: Add two zeroes to the remainder, making it 6500.
Step 7: Now, bring down a pair of zeros, making the new dividend 6500.
Step 8: We continue the process to find the new divisor and quotient, refining the decimal further.
The result is approximately 44.72136.
Square Root of 2001 by Approximation Method
The approximation method is another method for finding the 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 2001 using the approximation method.
Step 1: Now we have to find the closest perfect square of √2001. The smallest perfect square less than 2001 is 1936, and the largest perfect square greater than 2001 is 2025. √2001 falls somewhere between 44 and 45.
Step 2: Now we need to apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square)
Using the formula: (2001 - 1936) / (2025 - 1936) = 65 / 89 ≈ 0.7303 Adding this to the smaller square root, 44 + 0.7303 ≈ 44.7303, so the square root of 2001 is approximately 44.72136.
Common Mistakes and How to Avoid Them in the Square Root of 2001
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 typically consider only the positive square root.
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 children make. To resolve this, we need to teach children that simplifying the numbers inside the square root is important before moving on to the next step.
For example: √(12+24) = √12 + √24 is incorrect. The correct way is √(12+24) = √36 = 6.
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 ≈ 7.071.
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 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 a wrong answer. This may happen in the subtraction or elsewhere.
Square Root of 2001 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √2001?
The area of the square is approximately 2001 square units.
Explanation
The area of the square = side².
The side length is given as √2001.
Area of the square = (√2001)² = 2001.
Therefore, the area of the square box is approximately 2001 square units.
Problem 2
A square-shaped building measuring 2001 square feet is built; if each of the sides is √2001, what will be the square feet of half of the building?
1000.5 square feet
Explanation
We can divide the given area by 2 as the building is square-shaped.
Dividing 2001 by 2 = 1000.5.
So half of the building measures 1000.5 square feet.
Problem 3
Calculate √2001 x 5.
Approximately 223.6068
Explanation
The first step is to find the square root of 2001, which is approximately 44.72136.
The second step is to multiply 44.72136 by 5.
So 44.72136 x 5 = 223.6068.
Problem 4
What will be the square root of (2001 + 24)?
The square root is approximately 45.61798.
Explanation
To find the square root, we need to find the sum of (2001 + 24). 2001 + 24 = 2025, and then √2025 = 45.
Therefore, the square root of (2001 + 24) is ±45.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √2001 units and the width ‘w’ is 38 units.
The perimeter of the rectangle is approximately 165.44272 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√2001 + 38) = 2 × (44.72136 + 38) = 2 × 82.72136 = 165.44272 units.
FAQ on Square Root of 2001
1.What is √2001 in its simplest form?
2.Mention the factors of 2001.
3.Calculate the square of 2001.
4.Is 2001 a prime number?
5.2001 is divisible by?
6.How does learning Algebra help students in Singapore make better decisions in daily life?
7.How can cultural or local activities in Singapore support learning Algebra topics such as Square Root of 2001?
8.How do technology and digital tools in Singapore support learning Algebra and Square Root of 2001?
9.Does learning Algebra support future career opportunities for students in Singapore?
Important Glossaries for the Square Root of 2001
- Square root: A square root is the inverse operation of squaring a number. For example, if 4² = 16, then √16 = 4.
- Irrational number: An irrational number is a number that cannot be written as a simple fraction, meaning it cannot be expressed as p/q, where p and q are integers and q ≠ 0.
- Principal square root: A number has both positive and negative square roots, but the positive square root is typically used in real-world applications. This is known as the principal square root.
- Long division method: A method used to find the square root of non-perfect squares by dividing numbers into pairs or groups and solving iteratively.
- Decimal approximation: It refers to expressing an irrational number like the square root of a non-perfect square as a decimal, which is usually rounded to a certain number of decimal places.
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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
: He loves to play the quiz with kids through algebra to make kids love it.
