118 LearnersLast updated on May 26th, 2025
Square Root of 580
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 580.
What is the Square Root of 580?
The square root is the inverse of the square of the number. 580 is not a perfect square. The square root of 580 is expressed in both radical and exponential form. In the radical form, it is expressed as √580, whereas (580)^(1/2) in the exponential form. √580 ≈ 24.08319, 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 580
The prime factorization method is used for perfect square numbers. However, the prime factorization method is not generally used for non-perfect square numbers where long-division and approximation methods are more applicable. Let us now learn the following methods:
- Prime factorization method
- Long division method
- Approximation method
Square Root of 580 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 580 is broken down into its prime factors.
Step 1: Finding the prime factors of 580 Breaking it down, we get 2 x 2 x 5 x 29: 2^2 x 5^1 x 29^1
Step 2: Now we found out the prime factors of 580. The second step is to make pairs of those prime factors. Since 580 is not a perfect square, therefore the digits of the number can’t be grouped in pairs completely.
Therefore, calculating √580 using prime factorization gives us an approximation.
Square Root of 580 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 numbers surrounding 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 580, we need to group it as 80 and 5.
Step 2: Now we need to find n whose square is close to or equal to 5. We can take n as ‘2’ because 2 x 2 = 4 is lesser than 5. Now the quotient is 2, and after subtracting 4 from 5, the remainder is 1.
Step 3: Now let us bring down 80, making it the new dividend. Double the old divisor (which was 2) to get 4, which will be part of our new divisor.
Step 4: We now need to determine a digit as n to make the new divisor (4n) such that 4n x n is less than or equal to 180. Let n be 2, making 42 x 2 = 84.
Step 5: Subtract 84 from 180, getting a remainder of 96.
Step 6: Since the dividend is less than the divisor, we need to add a decimal point to the quotient. Adding the decimal point allows us to add two zeroes to the dividend. Now the new dividend is 9600.
Step 7: Continue with the long division steps, finding the next n and performing the subtraction until an accurate decimal approximation is achieved.
So the square root of √580 is approximately 24.08.
Square Root of 580 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 580 using the approximation method.
Step 1: Now we have to find the closest perfect square roots surrounding √580. The smallest perfect square less than 580 is 576, and the largest perfect square greater than 580 is 625. √580 falls somewhere between 24 and 25.
Step 2: Now we need to apply the formula: (Given number - smaller perfect square) / (larger perfect square - smaller perfect square) Using the formula: (580 - 576) / (625 - 576) = 4 / 49 ≈ 0.0816 Adding this to the smaller square root gives us 24 + 0.0816 ≈ 24.0816, so the square root of 580 is approximately 24.0816.
Common Mistakes and How to Avoid Them in the Square Root of 580
Students often make mistakes while finding square roots, such as forgetting about the negative square root, skipping long division steps, 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 generally take only the positive square root, as it is the required one in most contexts.
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
Not using the square root symbol 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 next step.
For example, √(12 + 24) = √36, 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 ≈ 7.071, not 7.
Mistake 4
Confusing the square root symbol with the cube root
Students need to be taught the difference between cube root and square root constantly 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 a wrong answer. This may happen in subtraction or elsewhere in the process.
Square Root of 580 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √580?
The area of the square box is approximately 580 square units.
Explanation
The area of the square = side^2.
The side length is given as √580.
Area of the square = side^2 = √580 x √580 = 580.
Therefore, the area of the square box is approximately 580 square units.
Problem 2
A square-shaped building measuring 580 square feet is built; if each of the sides is √580, what will be the square feet of half of the building?
290 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 580 by 2, we get 290.
So half of the building measures 290 square feet.
Problem 3
Calculate √580 x 5.
Approximately 120.42
Explanation
The first step is to find the square root of 580, which is approximately 24.08.
The second step is to multiply 24.08 by 5.
So, 24.08 x 5 ≈ 120.42.
Problem 4
What will be the square root of (558 + 22)?
The square root is approximately 24.08
Explanation
To find the square root, we need to find the sum of (558 + 22). 558 + 22 = 580, and √580 ≈ 24.08.
Therefore, the square root of (558 + 22) is approximately 24.08.
Problem 5
Find the perimeter of a rectangle if its length ‘l’ is √580 units and the width ‘w’ is 20 units.
The perimeter of the rectangle is approximately 88.16 units.
Explanation
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√580 + 20) = 2 × (24.08 + 20) = 2 × 44.08 ≈ 88.16 units.
FAQ on Square Root of 580
1.What is √580 in its simplest form?
2.Mention the factors of 580.
3.Calculate the square of 580.
4.Is 580 a prime number?
5.580 is divisible by?
6.How does learning Algebra help students in Saudi Arabia make better decisions in daily life?
7.How can cultural or local activities in Saudi Arabia support learning Algebra topics such as Square Root of 580?
8.How do technology and digital tools in Saudi Arabia support learning Algebra and Square Root of 580?
9.Does learning Algebra support future career opportunities for students in Saudi Arabia?
Important Glossaries for the Square Root of 580
- Square root: A square root is the inverse of a square. 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, but it is usually the positive square root that is used in real-world applications. This is known as the principal square root.
- 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.
- Approximation: The process of finding a value that is close to the actual value, often used when dealing with irrational numbers.
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About BrightChamps in Saudi Arabia
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.
