102 LearnersLast updated on May 26th, 2025
Square Root of 3589
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 3589.
What is the Square Root of 3589?
The square root is the inverse of the square of a number. 3589 is not a perfect square. The square root of 3589 is expressed in both radical and exponential form. In radical form, it is expressed as √3589, whereas (3589)^(1/2) in exponential form. √3589 ≈ 59.87098, 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 3589
The prime factorization method is used for perfect square numbers. However, the prime factorization method is not used for non-perfect square numbers where 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 3589 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 3589 is broken down into its prime factors:
Step 1: Finding the prime factors of 3589. Breaking it down, we find that 3589 is a prime number and cannot be factored into smaller prime numbers.
Step 2: Since 3589 is a prime number, it cannot be broken into pairs for the prime factorization method. Therefore, calculating 3589 using prime factorization is not feasible.
Square Root of 3589 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 3589, we need to group it as 35 and 89.
Step 2: Now, find n whose square is less than or equal to 35. We can say n as '5' because 5 x 5 = 25, which is less than 35. Subtract 25 from 35, and the remainder is 10.
Step 3: Bring down 89 to make it 1089. Add the old divisor with the same number, 5 + 5, to get 10, which will be our new divisor.
Step 4: The new divisor is 10n. We need to find the value of n such that 10n × n ≤ 1089. Let us consider n as 9; now 109 x 9 = 981.
Step 5: Subtract 981 from 1089. The difference is 108, and the quotient is 59.
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 10800.
Step 7: Find the new divisor, which is 598, because 598 x 8 = 4784.
Step 8: Subtract 4784 from 10800, resulting in 6016.
Step 9: Continue this process until you reach the desired decimal precision. The square root of √3589 ≈ 59.87098.
Square Root of 3589 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 3589 using the approximation method.
Step 1: Find the closest perfect squares around √3589. The smallest perfect square less than 3589 is 3481 (59^2), and the largest perfect square greater than 3589 is 3600 (60^2). √3589 falls between 59 and 60.
Step 2: Apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Using the formula: (3589 - 3481) / (3600 - 3481) ≈ 0.87098. Adding this result to the lower value, 59 + 0.87098 = 59.87098, so the square root of 3589 is approximately 59.87098.
Common Mistakes and How to Avoid Them in the Square Root of 3589
Students often make mistakes while finding the square root, such as forgetting about the negative square root or skipping steps in the long division method. Let us look at a few common mistakes students tend to make.
Mistake 1
Forgetting about the negative square root
It is important to remember that every positive number has both a positive and negative square root. However, when asked for "the square root," we typically refer to the positive root.
For example, √3589 ≈ 59.87098, but there is also -59.87098.
Square Root of 3589 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √3589?
The area of the square is approximately 128,800.16 square units.
Explanation
The area of the square = side^2.
The side length is given as √3589.
Area of the square = side^2 = √3589 × √3589 = 3589.
Therefore, the area of the square box is 3589 square units.
Problem 2
A square-shaped building measuring 3589 square feet is built; if each of the sides is √3589, what will be the square feet of half of the building?
1794.5 square feet
Explanation
We can divide the given area by 2 since the building is square-shaped.
Dividing 3589 by 2 gives us 1794.5.
So half of the building measures 1794.5 square feet.
Problem 3
Calculate √3589 × 5.
Approximately 299.3549
Explanation
The first step is to find the square root of 3589, which is approximately 59.87098.
The second step is to multiply 59.87098 by 5.
So 59.87098 × 5 ≈ 299.3549.
Problem 4
What will be the square root of (3489 + 100)?
The square root is 60.
Explanation
To find the square root, we need to find the sum of (3489 + 100). 3489 + 100 = 3589, and then √3589 ≈ 59.87098.
Rounding to the nearest whole number gives us 60.
Therefore, the square root of (3489 + 100) is approximately 60.
Problem 5
Find the perimeter of the rectangle if its length 'l' is √3589 units and the width 'w' is 50 units.
The perimeter of the rectangle is approximately 219.74196 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√3589 + 50) ≈ 2 × (59.87098 + 50) ≈ 2 × 109.87098 ≈ 219.74196 units.
FAQ on Square Root of 3589
1.What is √3589 in its simplest form?
2.Is 3589 a perfect square?
3.Calculate the square of 3589.
4.Is 3589 a prime number?
5.What is the decimal approximation of √3589?
6.How does learning Algebra help students in Bahrain make better decisions in daily life?
7.How can cultural or local activities in Bahrain support learning Algebra topics such as Square Root of 3589?
8.How do technology and digital tools in Bahrain support learning Algebra and Square Root of 3589?
9.Does learning Algebra support future career opportunities for students in Bahrain?
Important Glossaries for the Square Root of 3589
- Square root: A square root is the inverse of a square. Example: 5^2 = 25, and the inverse of the square is the square root, that is, √25 = 5.
- 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. For example, √2 is an irrational number.
- Prime number: A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. For example, 3589 is a prime number.
- Decimal approximation: A decimal approximation is an estimate of a number expressed in decimal form, often used for non-perfect squares or other irrational numbers. For example, √3589 ≈ 59.87098.
- Long division method: The long division method is a technique used to find the square root of non-perfect squares through a series of division steps, resulting in a decimal approximation.
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About BrightChamps in Bahrain
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.
