Last updated on May 26th, 2025
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.
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.
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:
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.
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.
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:
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.
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.
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.
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.
Calculate √583 × 3.
Approximately 72.411.
First, find the square root of 583, which is approximately 24.137.
Multiply this by 3: 24.137 × 3 ≈ 72.411.
What is the square root of (576 + 7)?
The square root is approximately 24.137.
To find the square root, first sum 576 + 7 = 583.
The square root of 583 is approximately 24.137.
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.
Perimeter = 2 × (length + width)
Perimeter = 2 × (√583 + 37) ≈ 2 × (24.137 + 37) ≈ 2 × 61.137 ≈ 122.274 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.
: He loves to play the quiz with kids through algebra to make kids love it.