137 LearnersLast updated on May 26th, 2025
Square Root of 562
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 various fields such as architecture, physics, and statistics. Here, we will discuss the square root of 562.
What is the Square Root of 562?
The square root is the inverse of the square of a number. 562 is not a perfect square. The square root of 562 is expressed in both radical and exponential form. In the radical form, it is expressed as √562, whereas (562)(1/2) in the exponential form. √562 ≈ 23.70654, 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 562
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 562 by Prime Factorization Method
The product of prime factors is the Prime factorization of a number. Now let us look at how 562 is broken down into its prime factors.
Step 1: Finding the prime factors of 562 Breaking it down, we get 2 x 281: 21 x 2811
Step 2: Now we found out the prime factors of 562. The second step is to make pairs of those prime factors. Since 562 is not a perfect square, the digits of the number can’t be grouped in pairs.
Therefore, calculating 562 using prime factorization to find its square root is not feasible.
Square Root of 562 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 around 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 562, we need to group it as 62 and 5.
Step 2: Now we need to find n whose square is less than or equal to 5. We can say n is 2 because 2 x 2 = 4, which is less than 5. Now the quotient is 2, and after subtracting 4 from 5, the remainder is 1.
Step 3: Now let us bring down 62, which is the new dividend. Add the old divisor (2) with itself to get 4, which will serve as the first part of our new divisor.
Step 4: The new divisor will be 4n. We need to find the value of n such that 4n x n is less than or equal to 162.
Step 5: Let n be 3. Then 43 x 3 = 129.
Step 6: Subtract 129 from 162; the difference is 33. The quotient is now 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 3300.
Step 8: We find that 474 x 7 = 3318.
Step 9: Subtracting 3318 from 3300 gives us a negative number, so we try 473 x 6 = 2838.
Step 10: Subtract 2838 from 3300, resulting in 462.
Step 11: Since we desire precision, continue the steps until achieving the desired decimal places.
Thus, the square root of √562 is approximately 23.706.
Square Root of 562 by Approximation Method
The approximation method is another method for finding square roots. It is an easy method to estimate the square root of a given number. Now let us learn how to find the square root of 562 using the approximation method.
Step 1: Now we have to find the closest perfect squares to √562. The smallest perfect square less than 562 is 529, and the largest perfect square more than 562 is 576. √562 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 (562 - 529) / (576 - 529) = 33 / 47 ≈ 0.702 Using this approximation, we identified the decimal portion of our square root. The next step is adding the integer part: 23 + 0.702 = 23.702.
Therefore, the approximate square root of 562 is 23.702.
Common Mistakes and How to Avoid Them in the Square Root of 562
Students often make mistakes while finding the square root, such as forgetting about the negative square root, skipping steps in the long division method, etc. Now let us look at a few of these mistakes in detail.
Mistake 1
Forgetting about the negative square root
It is important to remind students that a number has both positive and negative square roots. However, we usually consider only the positive square root as it is the most commonly used in real-world applications. For example: √50 ≈ 7.07, but there is also -7.07, which should not be ignored.
Square Root of 562 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √562?
The area of the square is approximately 562 square units.
Explanation
The area of a square = side2.
The side length is given as √562.
Area of the square = side2 = √562 x √562 = 562.
Therefore, the area of the square box is approximately 562 square units.
Problem 2
A square-shaped park measures 562 square meters. If each side is √562, what will be the area of half of the park?
281 square meters
Explanation
Since the park is square-shaped, we can divide the given area by 2 to find half the area.
Dividing 562 by 2 gives us 281.
So half of the park measures 281 square meters.
Problem 3
Calculate √562 x 5.
Approximately 118.5327
Explanation
The first step is to find the square root of 562, which is approximately 23.706.
The second step is to multiply 23.706 by 5.
So 23.706 x 5 ≈ 118.5327.
Problem 4
What will be the square root of (536 + 26)?
The square root is 24.
Explanation
To find the square root,
first calculate the sum of (536 + 26). 536 + 26 = 562, and then √562 ≈ 23.706.
Therefore, the square root of (536 + 26) is approximately ±23.706, rounded to ±24.
Problem 5
Find the perimeter of a rectangle if its length 'l' is √562 units and the width 'w' is 38 units.
The perimeter of the rectangle is approximately 123.412 units.
Explanation
The perimeter of a rectangle = 2 × (length + width).
Perimeter = 2 × (√562 + 38)
= 2 × (23.706 + 38) = 2 × 61.706 ≈ 123.412 units.
FAQ on Square Root of 562
1.What is √562 in its simplest form?
2.Mention the factors of 562.
3.Calculate the square of 562.
4.Is 562 a prime number?
5.562 is divisible by?
Important Glossaries for the Square Root of 562
- Square root: A square root is a value that, when multiplied by itself, gives the original number. Example: 42 = 16, and the inverse operation is the square root, √16 = 4.
- Irrational number: An irrational number cannot be written as a simple fraction or ratio of integers. Its decimal form is non-terminating and non-repeating.
- Principal square root: The principal square root of a number is its non-negative square root. For example, the principal square root of 9 is 3.
- Long division method: A technique used to find the square root of a non-perfect square by dividing and averaging.
- Approximation method: A method used to estimate the square root of a non-perfect square by comparing it to nearby perfect squares.
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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.
