122 LearnersLast updated on May 26th, 2025
Square Root of 569
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 569.
What is the Square Root of 569?
The square root is the inverse of the square of the number. 569 is not a perfect square. The square root of 569 is expressed in both radical and exponential form. In the radical form, it is expressed as √569, whereas 569^(1/2) in the exponential form. √569 ≈ 23.83275, 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 569
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 569 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 569 is broken down into its prime factors.
Step 1: Finding the prime factors of 569 Breaking it down, we get 569 = 1 x 569 (as 569 is a prime number).
Step 2: Since 569 is not a perfect square, calculating √569 using prime factorization is not feasible.
Square Root of 569 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 569, we need to group it as 69 and 5.
Step 2: Now we need to find n whose square is ≤ 5. We can say n is ‘2’ because 2 x 2 = 4, which is lesser than or equal to 5. Now the quotient is 2. After subtracting 4 from 5, the remainder is 1.
Step 3: Let us bring down 69, making the new dividend 169. Add the old divisor to the same number 2 + 2 = 4, which will be our new divisor.
Step 4: The new divisor will be 4n, where we need to find the value of n. Step 5: The next step is finding 4n × n ≤ 169. Let us consider n as 4; now, 44 x 4 = 176, which is too large. Try n as 3, 43 x 3 = 129.
Step 6: Subtract 129 from 169; the difference is 40. The quotient is 23.
Step 7: Since the dividend is less than the divisor, we add a decimal point, allowing us to add two zeroes to the dividend. Now the new dividend is 4000.
Step 8: Find the new divisor, which is 476 because 476 x 8 = 3808. Step 9: Subtracting 3808 from 4000, we get the result 192.
Step 10: Now the quotient is 23.8
Step 11: Continue this process until you get two numbers after the decimal point, unless the remainder becomes zero.
So the square root of √569 is approximately 23.83.
Square Root of 569 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 569 using the approximation method.
Step 1: Find the closest perfect squares of 569. The smallest perfect square less than 569 is 529, and the largest perfect square greater than 569 is 576. √569 falls somewhere between 23 and 24.
Step 2: Apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Using the formula (569 - 529) / (576 - 529) = 40 / 47 ≈ 0.851 Using the formula, we identified the decimal point of our square root. The next step is adding the value we got initially to the decimal number, which is 23 + 0.851 = 23.851, so the square root of 569 is approximately 23.85.
Common Mistakes and How to Avoid Them in the Square Root of 569
Students do make mistakes while finding the square root, such as forgetting about the negative square root or skipping long division methods. 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 will be taking only the positive square root, as it is the required one.
For example: √50 = 7.07; 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 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 second step.
For example: √(12+24) = √12 + √24 is the wrong method. The right way is √(12+24) = √36.
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, resulting in a wrong answer at the end of the sum. This may either happen in subtracting or elsewhere.
Square Root of 569 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √569?
The area of the square is approximately 569 square units.
Explanation
The area of the square = side².
The side length is given as √569.
Area of the square = side² = √569 x √569 = 569.
Therefore, the area of the square box is approximately 569 square units.
Problem 2
A square-shaped garden measuring 569 square feet is built. If each of the sides is √569, what will be the square feet of half of the garden?
284.5 square feet
Explanation
We can just divide the given area by 2 as the garden is square-shaped.
Dividing 569 by 2, we get 284.5.
So, half of the garden measures 284.5 square feet.
Problem 3
Calculate √569 x 6.
Approximately 142.9965
Explanation
The first step is to find the square root of 569, which is approximately 23.833.
The second step is to multiply 23.833 with 6. So, 23.833 x 6 ≈ 142.9965.
Problem 4
What will be the square root of (569 - 20)?
The square root is approximately 23.
Explanation
To find the square root, we need to find the difference of (569 - 20). 569 - 20 = 549, and then √549 ≈ 23.
Therefore, the square root of (569 - 20) is approximately ±23.
Problem 5
Find the perimeter of a rectangle if its length ‘l’ is √569 units and the width ‘w’ is 29 units.
The perimeter of the rectangle is approximately 105.666 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√569 + 29) = 2 × (23.833 + 29) = 2 × 52.833 = 105.666 units.
FAQ on Square Root of 569
1.What is √569 in its simplest form?
2.Mention the factors of 569.
3.Calculate the square of 569.
4.Is 569 a prime number?
5.569 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 569?
8.How do technology and digital tools in Australia support learning Algebra and Square Root of 569?
9.Does learning Algebra support future career opportunities for students in Australia?
Important Glossaries for the Square Root of 569
- Square root: A square root is the inverse of a square. For example, 5² = 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.
- Principal square root: A number has both positive and negative square roots. However, it is always the positive square root that has more prominence due to its uses in the real world. That is why it is also known as the principal square root.
- Prime number: A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. For example, 569 is a prime number.
- Decimal: If a number has a whole number and a fraction in a single number, then it is called a decimal. For example: 7.86, 8.65, and 9.42 are decimals.
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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.
Fun Fact
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