102 LearnersLast updated on May 26th, 2025
Square Root of 8712
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 such as vehicle design and finance. Here, we will discuss the square root of 8712.
What is the Square Root of 8712?
The square root is the inverse of the square of the number. 8712 is not a perfect square. The square root of 8712 is expressed in both radical and exponential form. In the radical form, it is expressed as √8712, whereas (8712)^(1/2) in the exponential form. √8712 ≈ 93.2978, 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 8712
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 8712 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 8712 is broken down into its prime factors.
Step 1: Finding the prime factors of 8712
Breaking it down, we get 2 x 2 x 2 x 3 x 3 x 11 x 11: 2^3 x 3^2 x 11^2
Step 2: Now we found out the prime factors of 8712. The next step is to make pairs of those prime factors. Since 8712 is not a perfect square, therefore the digits of the number can’t be grouped in pairs perfectly. Therefore, calculating the exact square root of 8712 using prime factorization requires further steps.
Square Root of 8712 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 8712, we need to group it as 87 and 12.
Step 2: Now we need to find n whose square is less than or equal to 87. We can say n is 9 because 9 x 9 = 81, which is less than 87. Now the quotient is 9, and after subtracting 87 - 81, the remainder is 6.
Step 3: Now let us bring down 12, making the new dividend 612. Add the old divisor with the same number 9 + 9 to get 18, which will be our new divisor.
Step 4: We need to find n such that 18n x n is less than or equal to 612. Let us consider n as 3, then 183 x 3 = 549.
Step 5: Subtract 549 from 612; the difference is 63, and the quotient is 93.
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 6300.
Step 7: Now we need to find the new divisor, which is 933, because 933 x 7 = 6531.
Step 8: Subtracting 6531 from 6300 gives us a result of -231, but we continue the process further to refine the decimal.
Step 9: The quotient continues to approximate to 93.2978.
Square Root of 8712 by Approximation Method
The approximation method is another way to find square roots. It is an easy method to find the square root of a given number. Let us now learn how to find the square root of 8712 using the approximation method.
Step 1: Now we have to find the closest perfect squares around 8712. The smallest perfect square below 8712 is 8100, and the largest perfect square above 8712 is 9216. √8712 falls somewhere between 90 and 96.
Step 2: Use the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square) Applying the formula: (8712 - 8100) / (9216 - 8100) ≈ 0.2978
Using the formula, we identify the decimal point of our square root. The next step is adding the initial integer value (90) to the decimal approximation, which gives us 90 + 3.2978 ≈ 93.2978, so the square root of 8712 is approximately 93.2978.
Common Mistakes and How to Avoid Them in the Square Root of 8712
Students often make mistakes while finding the square root, such as forgetting the negative square root or skipping steps in the long division method. Now, let's discuss a few common mistakes students make in detail.
Mistake 1
Forgetting about the negative square root
It is important to make students aware that a number has both positive and negative square roots. However, we typically consider only the positive square root in practical applications.
For example, √8712 ≈ ±93.2978, but we often use 93.2978.
Square Root of 8712 Examples
Problem 1
Can you help Alex find the area of a square box if its side length is given as √8712?
The area of the square is approximately 8712 square units.
Explanation
The area of the square = side².
The side length is given as √8712.
Area of the square = side² = √8712 × √8712 = 8712.
Therefore, the area of the square box is approximately 8712 square units.
Problem 2
A square-shaped garden measuring 8712 square feet is planned; if each of the sides is √8712, what will be the square feet of half of the garden?
4356 square feet
Explanation
We can divide the given area by 2 as the garden is square-shaped.
Dividing 8712 by 2 gives us 4356.
So half of the garden measures 4356 square feet.
Problem 3
Calculate √8712 × 5.
Approximately 466.489
Explanation
The first step is to find the square root of 8712, which is approximately 93.2978.
Then, multiply 93.2978 by 5.
So 93.2978 × 5 ≈ 466.489
Problem 4
What will be the square root of (8712 + 144)?
The square root is approximately 94.
Explanation
First, find the sum of 8712 + 144 = 8856.
Then find the square root of 8856. √8856 ≈ 94.
Therefore, the square root of (8712 + 144) is approximately ±94.
Problem 5
Find the perimeter of a rectangle if its length ‘l’ is √8712 units and the width ‘w’ is 38 units.
The perimeter of the rectangle is approximately 262.5956 units.
Explanation
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√8712 + 38) Perimeter ≈ 2 × (93.2978 + 38) ≈ 2 × 131.2978 ≈ 262.5956 units.
FAQ on Square Root of 8712
1.What is √8712 in its simplest form?
2.Mention the factors of 8712.
3.Calculate the square of 8712.
4.Is 8712 a prime number?
5.8712 is divisible by?
6.How does learning Algebra help students in Singapore make better decisions in daily life?
7.How can cultural or local activities in Singapore support learning Algebra topics such as Square Root of 8712?
8.How do technology and digital tools in Singapore support learning Algebra and Square Root of 8712?
9.Does learning Algebra support future career opportunities for students in Singapore?
Important Glossaries for the Square Root of 8712
- Square root: A square root is the inverse operation of squaring a number. 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.
- Principal square root: A number has both positive and negative square roots; however, it is typically the positive square root that is used in real-world applications. This is known as the principal square root.
- Prime factorization: The process of expressing a number as a product of its prime factors.
- Long division method: A step-by-step method used to find the square root of non-perfect square numbers, involving division and subtraction.
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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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