120 LearnersLast updated on May 26th, 2025
Square Root of 2005
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 2005.
What is the Square Root of 2005?
The square root is the inverse of the square of the number. 2005 is not a perfect square. The square root of 2005 is expressed in both radical and exponential form. In the radical form, it is expressed as √2005, whereas (2005)^(1/2) is in the exponential form. √2005 ≈ 44.778, 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 2005
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 2005 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 2005 is broken down into its prime factors.
Step 1: Finding the prime factors of 2005
Breaking it down, we get 5 x 401.
Step 2: Now we found out the prime factors of 2005. The second step is to make pairs of those prime factors. Since 2005 is not a perfect square, the digits of the number can’t be grouped in pairs. Therefore, calculating 2005 using prime factorization is impossible.
Square Root of 2005 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 2005, we need to group it as 05 and 20.
Step 2: Now we need to find n whose square is closest to 20. We can say n is 4 because 4 x 4 = 16, which is lesser than or equal to 20. Now the quotient is 4, and the remainder is 20 - 16 = 4.
Step 3: Now let us bring down 05, giving us a new dividend of 405. Add the old divisor with the same number: 4 + 4 = 8, which will be our new divisor.
Step 4: We need to find the largest possible digit x such that 8x * x ≤ 405. For x = 5, 85 * 5 = 425, which is more than 405. For x = 4, 84 * 4 = 336, which is less than 405.
Step 5: Subtract 336 from 405; the remainder is 69. Our quotient is now 44.
Step 6: 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 6900.
Step 7: Find the new divisor, 88, by adding 4 to the quotient, making it 88x. Determine x such that 88x * x ≤ 6900. For x = 7, 887 * 7 = 6209.
Step 8: Subtracting 6209 from 6900 gives us a remainder of 691.
Step 9: The quotient is now 44.7.
Step 10: Continue doing these steps until we get two numbers after the decimal point. Suppose if there are no decimal values, continue till the remainder is zero.
So the square root of √2005 is approximately 44.78.
Square Root of 2005 by Approximation Method
The approximation method is another method for finding square roots, and 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 2005 using the approximation method.
Step 1: Now we have to find the closest perfect square of √2005. The smallest perfect square less than 2005 is 1936 (44^2), and the largest perfect square more than 2005 is 2025 (45^2). √2005 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). (2005 - 1936) ÷ (2025 - 1936) = 69 ÷ 89 ≈ 0.775
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 + 0.775 ≈ 44.775, so the square root of 2005 is approximately 44.775.
Common Mistakes and How to Avoid Them in the Square Root of 2005
Students do make mistakes while finding the square root, like 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 = 7.071, there is also -7.071, 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 the 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 ≈ 7.071.
Mistake 4
Confusing the square root symbol with the cube root
Students need to be taught the difference between the 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 sum. This may either happen in subtracting or elsewhere.
Square root of 2005 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √1805?
The area of the square is 1805 square units.
Explanation
The area of the square = side².
The side length is given as √1805.
Area of the square = side² = √1805 x √1805 = 1805.
Therefore, the area of the square box is 1805 square units.
Problem 2
A square-shaped building measuring 2005 square feet is built; if each of the sides is √2005, what will be the square feet of half of the building?
1002.5 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 2005 by 2, we get 1002.5.
So half of the building measures 1002.5 square feet.
Problem 3
Calculate √2005 x 5.
Approximately 223.89
Explanation
The first step is to find the square root of 2005, which is approximately 44.778.
The second step is to multiply 44.778 by 5.
So 44.778 x 5 ≈ 223.89.
Problem 4
What will be the square root of (1805 + 200)?
The square root is approximately 45.
Explanation
To find the square root, we need to find the sum of (1805 + 200). 1805 + 200 = 2005, and then √2005 ≈ 44.778.
Therefore, the square root of (1805 + 200) is approximately ±44.778.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √1805 units and the width ‘w’ is 40 units.
We find the perimeter of the rectangle as approximately 176.56 units.
Explanation
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√1805 + 40) = 2 × (42.5 + 40) = 2 × 82.5 ≈ 165 units.
FAQ on Square Root of 2005
1.What is √2005 in its simplest form?
2.Mention the factors of 2005.
3.Calculate the square of 2005.
4.Is 2005 a prime number?
5.2005 is divisible by?
6.How does learning Algebra help students in Canada make better decisions in daily life?
7.How can cultural or local activities in Canada support learning Algebra topics such as Square Root of 2005?
8.How do technology and digital tools in Canada support learning Algebra and Square Root of 2005?
9.Does learning Algebra support future career opportunities for students in Canada?
Important Glossaries for the Square Root of 2005
- 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, 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; however, it is always the positive square root that has more prominence due to its uses in the real world. That is the reason it is also known as the principal square root.
- Decimal: If a number has a whole number and a fraction in a single number, then it is called a decimal. For example, 7.86, 8.65, and 9.42 are decimals.
- Long division method: A technique used to find the square root of a non-perfect square by repeated division and subtraction.
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Jaskaran Singh Saluja
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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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