Last updated on May 26th, 2025
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.
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.
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:
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.
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.
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.
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.
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.
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.
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
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.
Calculate √569 x 6.
Approximately 142.9965
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.
What will be the square root of (569 - 20)?
The square root is approximately 23.
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.
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.
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√569 + 29) = 2 × (23.833 + 29) = 2 × 52.833 = 105.666 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.
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