135 LearnersLast updated on May 26th, 2025
Square Root of 2000
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 2000.
What is the Square Root of 2000?
The square root is the inverse of the square of the number. 2000 is not a perfect square. The square root of 2000 is expressed in both radical and exponential form. In the radical form, it is expressed as √2000, whereas in the exponential form it is (2000)^(1/2). √2000 ≈ 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 2000
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 2000 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 2000 is broken down into its prime factors.
Step 1: Finding the prime factors of 2000
Breaking it down, we get 2 × 2 × 2 × 2 × 5 × 5 × 5: 2^4 × 5^3
Step 2: Now we found out the prime factors of 2000. The second step is to make pairs of those prime factors. Since 2000 is not a perfect square, the digits of the number can’t be grouped into pairs evenly. Therefore, calculating √2000 using prime factorization directly is not possible.
Square Root of 2000 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 2000, we need to group it as 00 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 × 4 = 16, which is less than or equal to 20. Now the quotient is 4. After subtracting 16 from 20, the remainder is 4.
Step 3: Bring down 00, making the new dividend 400. Double the current quotient, 4, to get 8, which will be part of our new divisor.
Step 4: We need to find a digit x such that 8x × x ≤ 400. Let us consider x as 4, now 84 × 4 = 336.
Step 5: Subtract 336 from 400, and the remainder is 64. The 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 6400.
Step 7: The new divisor will be 88 (from 84) plus the next digit x. We need to find x such that 88x × x ≤ 6400. Let us consider x as 7, now 887 × 7 = 6209.
Step 8: Subtract 6209 from 6400, and the remainder is 191.
Step 9: The quotient is now 44.7.
Step 10: Continue doing these steps until we get two numbers after the decimal point or until the remainder is zero.
So the square root of √2000 is approximately 44.72.
Square Root of 2000 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 2000 using the approximation method.
Step 1: Now we have to find the closest perfect squares of √2000. The smallest perfect square less than 2000 is 1936 (44^2) and the largest perfect square more than 2000 is 2025 (45^2). √2000 falls somewhere between 44 and 45.
Step 2: Now we need to apply the formula that is (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square).
Using the formula (2000 - 1936) ÷ (2025 - 1936) = 64 ÷ 89 ≈ 0.7191. Adding this to 44, we get 44 + 0.7191 ≈ 44.72, so the square root of 2000 is approximately 44.72.
Common Mistakes and How to Avoid Them in the Square Root of 2000
Students do make mistakes while finding the square root, such as forgetting about the negative square root or skipping steps in long division. 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 often focus on the positive square root due to its applications.
For example: √50 = ±7.071, but for practical purposes, we usually use the positive value.
Mistake 2
Not adding the square root symbol in proper places
Not using the square root properly is another mistake that students make. To resolve this, we need to teach students that simplifying the numbers inside the square root is important before proceeding.
For example: √(12+24) = √36 is correct, not √12 + √24.
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 ≈ 7.071067, not 7.
Mistake 4
Confusing the square root symbol with the cube root
Students need to be taught the difference between the cube root and the square root, 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, which results in the wrong answer at the end. This may happen during subtraction or elsewhere.
Square root of 2000 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √2000?
The area of the square is 2000 square units.
Explanation
The area of the square = side^2.
The side length is given as √2000
Area of the square = side^2 = √2000 × √2000 = 2000.
Therefore, the area of the square box is 2000 square units.
Problem 2
A square-shaped building measuring 2000 square feet is built; if each of the sides is √2000, what will be the square feet of half of the building?
1000 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 2000 by 2 gives us 1000.
So half of the building measures 1000 square feet.
Problem 3
Calculate √2000 × 5.
223.6068
Explanation
The first step is to find the square root of 2000, which is approximately 44.72.
The second step is to multiply 44.72 by 5.
So, 44.72 × 5 = 223.6068.
Problem 4
What will be the square root of (2000 + 25)?
The square root is approximately 45.
Explanation
To find the square root, we need to find the sum of (2000 + 25). 2000 + 25 = 2025, and √2025 = 45.
Therefore, the square root of (2000 + 25) is ±45.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √2000 units and the width ‘w’ is 38 units.
We find the perimeter of the rectangle as 165.4427 units.
Explanation
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√2000 + 38) = 2 × (44.72136 + 38) = 2 × 82.72136 = 165.4427 units.
FAQ on Square Root of 2000
1.What is √2000 in its simplest form?
2.Mention the factors of 2000.
3.Calculate the square of 2000.
4.Is 2000 a prime number?
5.2000 is divisible by?
6.How does learning Algebra help students in Vietnam make better decisions in daily life?
7.How can cultural or local activities in Vietnam support learning Algebra topics such as Square Root of 2000?
8.How do technology and digital tools in Vietnam support learning Algebra and Square Root of 2000?
9.Does learning Algebra support future career opportunities for students in Vietnam?
Important Glossaries for the Square Root of 2000
- Square root: A square root is the inverse of a square. For example, 4^2 = 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 why it is known as the principal square root.
- Prime factorization: Prime factorization is expressing a number as the product of its prime factors.
- Decimal: If a number has a whole number and a fraction in a single number, it is called a decimal. For example, 7.86, 8.65, and 9.42 are decimals.
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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.
