120 LearnersLast updated on May 26th, 2025
Square Root of 583
If a number is multiplied by itself, the result is a square. The inverse operation is finding the square root. Square roots are used in various fields, such as engineering and finance. Here, we will discuss the square root of 583.
What is the Square Root of 583?
The square root is the inverse of squaring a number. 583 is not a perfect square. The square root of 583 is expressed in both radical and exponential forms. In the radical form, it is expressed as √583, whereas in the exponential form, it is (583)¹/₂. √583 ≈ 24.137, which is an irrational number because it cannot be expressed as a ratio of two integers.
Finding the Square Root of 583
The prime factorization method is typically used for perfect square numbers. However, for non-perfect square numbers, methods like the long-division method and approximation method are used. Let us now learn the following methods:
- Long division method
- Approximation method
Square Root of 583 by Long Division Method
The long division method is used for non-perfect square numbers. Let's learn how to find the square root using the long division method, step by step:
Step 1: Group the numbers from right to left. For 583, we group it as 83 and 5.
Step 2: Find n whose square is less than or equal to 5. We select n as 2 because 2² = 4 ≤ 5. Subtracting 4 from 5, the remainder is 1, and the quotient is 2.
Step 3: Bring down 83 to make it 183. Add the old divisor to itself, 2 + 2 = 4, which will be the new divisor.
Step 4: Estimate n such that 4n × n ≤ 183. Choose n as 4, so 44 × 4 = 176.
Step 5: Subtract 176 from 183, resulting in a remainder of 7. The quotient is 24.
Step 6: Add a decimal point and bring down a pair of zeroes, making it 700.
Step 7: Find the new divisor, 48, because 484 × 4 = 1936, which fits.
Step 8: Repeat the process to achieve the desired precision.
So the square root of √583 ≈ 24.137.
Square Root of 583 by Approximation Method
The approximation method is another way to find square roots, which is relatively easy. Let's find the square root of 583 using this method.
Step 1: Identify the perfect squares around 583. The closest perfect squares are 576 (24²) and 625 (25²). √583 lies between 24 and 25.
Step 2: Apply the formula: (Given number - smaller perfect square) ÷ (larger perfect square - smaller perfect square) (583 - 576) ÷ (625 - 576) = 7 ÷ 49 ≈ 0.143
Step 3: Add this to the smaller whole number: 24 + 0.143 = 24.143, so the approximate square root of 583 is 24.143.
Common Mistakes and How to Avoid Them in the Square Root of 583
Students often make mistakes when finding square roots, such as forgetting the negative square root or skipping steps in the long division method. Here are some common mistakes:
Mistake 1
Forgetting about the negative square root
Students should know that every positive number has both positive and negative square roots. However, we usually consider only the positive square root unless otherwise specified.
For example, √49 = ±7.
Mistake 2
Not using the square root symbol correctly
Another common mistake is misplacing the square root symbol. Teach students to simplify terms under the square root before proceeding.
For example, √(25 + 9) ≠ √25 + √9; it simplifies to √34.
Mistake 3
Misidentifying the square root of a non-perfect square
It's essential to simplify and approximate correctly for non-perfect squares.
For example, √50 ≈ 7.071, not exactly 7.
Mistake 4
Confusing square root with cube root
Students often mix up square and cube roots. Reinforce the difference: √8 ≠ ∛8; the former is a square root, and the latter is a cube root.
Mistake 5
Errors in the long division method
The long division method involves many steps, and errors can occur if steps are skipped. Ensure students follow each step carefully to avoid mistakes.
Square Root of 583 Examples
Problem 1
Can you help Emma find the area of a square if its side length is given as √583?
The area of the square is approximately 583 square units.
Explanation
The area of a square is calculated as side².
The side length is given as √583.
Area = side² = √583 × √583 = 583.
Therefore, the area of the square is approximately 583 square units.
Problem 2
A square-shaped garden measuring 583 square feet is built; if each side is √583, what will be the square feet of half of the garden?
Approximately 291.5 square feet.
Explanation
Divide the area by 2, as the garden is square-shaped. 583 ÷ 2 = 291.5.
Half of the garden measures approximately 291.5 square feet.
Problem 3
Calculate √583 × 3.
Approximately 72.411.
Explanation
First, find the square root of 583, which is approximately 24.137.
Multiply this by 3: 24.137 × 3 ≈ 72.411.
Problem 4
What is the square root of (576 + 7)?
The square root is approximately 24.137.
Explanation
To find the square root, first sum 576 + 7 = 583.
The square root of 583 is approximately 24.137.
Problem 5
Find the perimeter of a rectangle if its length ‘l’ is √583 units and its width ‘w’ is 37 units.
The perimeter is approximately 122.274 units.
Explanation
Perimeter = 2 × (length + width)
Perimeter = 2 × (√583 + 37) ≈ 2 × (24.137 + 37) ≈ 2 × 61.137 ≈ 122.274 units.
FAQ on Square Root of 583
1.What is √583 in its simplest form?
2.What are the factors of 583?
3.Calculate the square of 583.
4.Is 583 a prime number?
5.583 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 583?
8.How do technology and digital tools in Vietnam support learning Algebra and Square Root of 583?
9.Does learning Algebra support future career opportunities for students in Vietnam?
Important Glossaries for the Square Root of 583
- Square root: A square root of a number is a value that, when multiplied by itself, gives the original number. Example: √9 = 3 because 3 × 3 = 9.
- Irrational number: A number that cannot be expressed as a simple fraction, such as √2 or √583.
- Approximation method: A technique to find an approximate value for the square root of a number, often used for non-perfect squares.
- Prime number: A number greater than 1 that has no positive divisors other than 1 and itself. Example: 2, 3, 5, 7, 11, 13, ...
- Long division method: A step-by-step approach used to find the square root of a number, especially useful for non-perfect squares.
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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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