Last updated on May 26th, 2025
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.
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.
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:
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.
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.
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.
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.
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.
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.
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
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.
Calculate √2001 x 5.
Approximately 223.6068
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.
What will be the square root of (2001 + 24)?
The square root is approximately 45.61798.
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.
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.
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√2001 + 38) = 2 × (44.72136 + 38) = 2 × 82.72136 = 165.44272 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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