135 LearnersLast updated on May 26th, 2025
Square Root of 2023
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 2023.
What is the Square Root of 2023?
The square root is the inverse of the square of a number. 2023 is not a perfect square. The square root of 2023 is expressed in both radical and exponential form. In the radical form, it is expressed as √2023, whereas (2023)^(1/2) in the exponential form. √2023 ≈ 44.94, 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 2023
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 2023 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 2023 is broken down into its prime factors:
Step 1: Finding the prime factors of 2023.
Breaking it down, we get 7 x 17 x 17: 7^1 x 17^2.
Step 2: Now we found out the prime factors of 2023. The second step is to make pairs of those prime factors. Since 2023 is not a perfect square, the digits of the number can’t be grouped perfectly in pairs. Therefore, calculating 2023 using prime factorization is not straightforward.
Square Root of 2023 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, group the numbers from right to left. For 2023, group it as 23 and 20.
Step 2: Find n whose square is less than or equal to 20. Here, n is 4 because 4^2 = 16 and is less than 20. Now the quotient is 4, and after subtracting 16 from 20, the remainder is 4.
Step 3: Bring down 23, making the new dividend 423. Add the old divisor to the same number (4 + 4) to get 8, which will be our new divisor.
Step 4: Find the greatest digit x such that (8x)x ≤ 423. Here, x is 5, because 85 x 5 = 425 is the closest and less than or equal to 423.
Step 5: Subtract 425 from 423 to get a remainder of -2 (indicating we should adjust x to 4).
Step 6: Continue the process by estimating further digits after the decimal point.
Thus, the square root of 2023 is approximately 44.94.
Square Root of 2023 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 2023 using the approximation method.
Step 1: Identify the closest perfect squares around 2023. The smallest perfect square less than 2023 is 2025, and the largest less than 2023 is 1936. √2023 is between 44 and 45.
Step 2: Apply the formula: (Given number - nearest lower perfect square) / (nearest higher perfect square - nearest lower perfect square) (2023 - 1936) / (2025 - 1936) = 87/89 ≈ 0.978
Step 3: Add the decimal to the lower square root estimate: 44 + 0.978 = 44.978, so the square root of 2023 is approximately 44.98.
Common Mistakes and How to Avoid Them in the Square Root of 2023
Students make mistakes while finding the square root, such as forgetting about the negative square root or skipping steps in the long division method. Let's look at a few of these mistakes in detail.
Mistake 1
Forgetting about the negative square root
A number has both positive and negative square roots. However, we usually consider only the positive square root as it is most often required.
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
Incorrect use of the square root symbol is another common mistake. Teach that simplifying the numbers inside the square root is essential before moving to subsequent steps.
For example: √(12+24) = √36, not √12 + √24.
Mistake 3
Not finding the correct value of a non-perfect square
The first step is to accurately estimate or calculate the numbers inside the square root. This prevents mistakes when identifying the approximate value.
For example: √50 ≠ 7, the correct approximation is √50 ≈ 7.071.
Mistake 4
Confusing the square root symbol with the cube root
Students should be taught the difference between cube roots and square roots.
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. Many students might skip a step accidentally, resulting in a wrong answer. This may happen during subtraction or elsewhere.
Square Root of 2023 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √2023?
The area of the square is approximately 2023 square units.
Explanation
The area of the square = side^2.
The side length is given as √2023.
Area of the square = (√2023) x (√2023) = 2023.
Therefore, the area of the square box is approximately 2023 square units.
Problem 2
A square-shaped plot measuring 2023 square feet is built; if each of the sides is √2023, what will be the square feet of half of the plot?
1011.5 square feet
Explanation
To find half of the plot, divide the given area by 2 as the plot is square-shaped.
Dividing 2023 by 2 = 1011.5.
So half of the plot measures 1011.5 square feet.
Problem 3
Calculate √2023 x 5.
Approximately 224.7
Explanation
First, find the square root of 2023, which is approximately 44.94.
Then multiply 44.94 by 5.
So 44.94 x 5 ≈ 224.7.
Problem 4
What will be the square root of (2025 - 2)?
The square root is approximately 44.89.
Explanation
To find the square root, first calculate the difference (2025 - 2) = 2023.
Then, √2023 ≈ 44.89.
Therefore, the square root of (2025 - 2) is approximately ±44.89.
Problem 5
Find the perimeter of a rectangle if its length ‘l’ is √2023 units and the width ‘w’ is 38 units.
The perimeter of the rectangle is approximately 165.88 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√2023 + 38) = 2 × (44.94 + 38) ≈ 2 × 82.94 ≈ 165.88 units.
FAQ on Square Root of 2023
1.What is √2023 in its simplest form?
2.Mention the factors of 2023.
3.Calculate the square of 2023.
4.Is 2023 a prime number?
5.2023 is divisible by?
6.How does learning Algebra help students in Australia make better decisions in daily life?
7.How can cultural or local activities in Australia support learning Algebra topics such as Square Root of 2023?
8.How do technology and digital tools in Australia support learning Algebra and Square Root of 2023?
9.Does learning Algebra support future career opportunities for students in Australia?
Important Glossaries for the Square Root of 2023
- 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.
- Perfect square: A number that is the square of an integer. For example, 25 is a perfect square because it is 5^2.
- Long division method: A technique used to find the square root of a number by dividing it into smaller, more manageable parts.
- Approximation method: A method to estimate the square root of a number by identifying two perfect squares between which the number lies.
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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.
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