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113 LearnersLast updated on March 21st, 2025
Square Root of 559
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 559.
What is the Square Root of 559?
The square root is the inverse of the square of the number. 559 is not a perfect square. The square root of 559 is expressed in both radical and exponential form. In the radical form, it is expressed as √559, whereas (559)(1/2) in the exponential form. √559 ≈ 23.629, 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 559
The prime factorization method is used for perfect square numbers. However, the prime factorization method is not used for non-perfect square numbers where the 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 559 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 559 is broken down into its prime factors.
Step 1: Finding the prime factors of 559 Breaking it down, we get 13 x 43: 131 x 431
Step 2: Now we found out the prime factors of 559. The second step is to make pairs of those prime factors. Since 559 is not a perfect square, grouping the digits in pairs is not possible.
Therefore, calculating √559 using prime factorization is impractical.
Square Root of 559 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 559, we need to group it as 59 and 5.
Step 2: Now we need to find n whose square is 5. We can say n as ‘2’ because 2 x 2 is less than or equal to 5. Now the quotient is 2; after subtracting 4 from 5, the remainder is 1.
Step 3: Now let us bring down 59, which is the new dividend. Add the old divisor with the same number: 2 + 2 = 4, which will be our new divisor.
Step 4: The new divisor will be the sum of the dividend and quotient. Now we get 4n as the new divisor; we need to find the value of n.
Step 5: The next step is finding 4n x n ≤ 159. Let us consider n as 3; now 43 x 3 = 129.
Step 6: Subtract 129 from 159; the difference is 30, and the quotient is 23.
Step 7: 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 3000.
Step 8: Now we need to find the new divisor that is 7 because 473 x 7 = 3311. Step 9: Subtracting 3311 from 3000, we get the result -311.
Step 10: Now the quotient is 23.6.
Step 11: Continue doing these steps until we get two numbers after the decimal point. Suppose if there are no decimal values, continue till the remainder is zero.
So the square root of √559 ≈ 23.63.
Square Root of 559 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 559 using the approximation method.
Step 1: Now we have to find the closest perfect square of √559. The smallest perfect square less than 559 is 529, and the largest perfect square greater than 559 is 576. √559 falls somewhere between 23 and 24.
Step 2: Now we need to apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Using the formula (559 - 529) ÷ (576 - 529) = 0.638.
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 + 0.638 = 23.638.
So the square root of 559 is approximately 23.638.
Common Mistakes and How to Avoid Them in the Square Root of 559
Students do make mistakes while finding the square root, like forgetting about the negative square root and skipping long division methods, 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 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.
Square root of 559 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √538?
The area of the square is 538 square units.
Explanation
The area of the square = side2
The side length is given as √538.
Area of the square = side2 = √538 x √538 = 538.
Therefore, the area of the square box is 538 square units.
Problem 2
A square-shaped building measuring 559 square feet is built; if each of the sides is √559, what will be the square feet of half of the building?
279.5 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 559 by 2 gives us 279.5.
So half of the building measures 279.5 square feet.
Problem 3
Calculate √559 x 5.
118.145
Explanation
The first step is to find the square root of 559, which is approximately 23.629.
The second step is to multiply 23.629 by 5.
So, 23.629 x 5 = 118.145.
Problem 4
What will be the square root of (529 + 30)?
The square root is 24.
Explanation
To find the square root,
we need to find the sum of (529 + 30). 529 + 30 = 559, and then √559 ≈ 23.63.
However, the square root of 576 (which is closest to 559) is 24.
Therefore, the square root of (529 + 30) is approximately 23.63 but can be rounded to 24 for simplicity.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √559 units and the width ‘w’ is 39 units.
We find the perimeter of the rectangle as 125.258 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√559 + 39)
= 2 × (23.629 + 39)
= 2 × 62.629 = 125.258 units.
FAQ on Square Root of 559
1.What is √559 in its simplest form?
2.Mention the factors of 559.
3.Calculate the square of 559.
4.Is 559 a prime number?
5.559 is divisible by?
Important Glossaries for the Square Root of 559
- Square root: A square root is the inverse of a square. For example, 42 = 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.
- Prime factorization: The process of expressing a number as the product of its prime factors. For example, the prime factorization of 559 is 13 x 43.
- Long division method: A method used to find the square root of non-perfect squares through division, involving a series of steps to approximate the square root.
- Decimal: A number that has a whole number and a fractional part separated by a decimal point, for example, 23.629.
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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
: He loves to play the quiz with kids through algebra to make kids love it.
