124 LearnersLast updated on May 26th, 2025
Square Root of 831
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 831.
What is the Square Root of 831?
The square root is the inverse of the square of the number. 831 is not a perfect square. The square root of 831 is expressed in both radical and exponential form. In the radical form, it is expressed as √831, whereas (831)^(1/2) in the exponential form. √831 ≈ 28.82707, 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 831
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 831 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now, let us look at how 831 is broken down into its prime factors.
Step 1: Finding the prime factors of 831 Breaking it down, we get 3 x 277: 3^1 x 277^1
Step 2: Now we found out the prime factors of 831. The second step is to make pairs of those prime factors. Since 831 is not a perfect square, the digits of the number can’t be grouped in pairs.
Therefore, calculating 831 using prime factorization is not feasible for finding an exact square root.
Square Root of 831 by Long Division Method
The long division method is particularly used for non-perfect square numbers. In this method, we 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 831, we need to group it as 31 and 8.
Step 2: Now we need to find n whose square is less than or equal to 8. We can say n is ‘2’ because 2 x 2 = 4, which is less than 8. Now the quotient is 2. After subtracting 4 from 8, the remainder is 4.
Step 3: Now let us bring down 31, making the new dividend 431. Add the old divisor with the same number: 2 + 2 = 4, which will be our new divisor.
Step 4: The new divisor will be 4n. We need to find the value of n such that 4n x n ≤ 431.
Step 5: The next step is finding 4n x n ≤ 431. Let n be 7, now 47 x 7 = 329.
Step 6: Subtract 329 from 431. The difference is 102, and the quotient is 27.
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. The new dividend is 10200.
Step 8: Now we need to find the new divisor. The trial divisor is 554 because 554 x 18 = 9972.
Step 9: Subtracting 9972 from 10200, we get 228.
Step 10: Now the quotient is 28.8.
Step 11: Continue doing these steps until we get two numbers after the decimal point. If there are no decimal values, continue till the remainder is zero.
So the square root of √831 is approximately 28.83.
Square Root of 831 by Approximation Method
The approximation method is another way 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 831 using the approximation method.
Step 1: Now we have to find the closest perfect square of √831.
The smallest perfect square less than 831 is 784, and the largest perfect square greater than 831 is 900. √831 falls somewhere between 28 and 30.
Step 2: Now we need to apply the formula that is (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square).
Using the formula (831 - 784) / (900 - 784) = 47 / 116 ≈ 0.405. Adding this to the lower perfect square root: 28 + 0.405 = 28.405.
The approximate square root of 831 is 28.83 when refined further.
Common Mistakes and How to Avoid Them in the Square Root of 831
Students make mistakes while finding the square root, such as forgetting about the negative square root and skipping steps in the long division method. Now let us look at a few of those mistakes 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 will focus on the positive square root, as it is typically required.
For example: √50 = 7.071, but there is also -7.071, which should not be forgotten.
Mistake 2
Not adding the square root symbol in proper places
Incorrect use of the square root symbol is another mistake. To resolve this, we need to teach students that simplifying the numbers inside the square root is important before proceeding.
For example: √(12 + 24) = √12 + √24 is incorrect. The correct way is √(12 + 24) = √36 = 6.
Mistake 3
Not finding the correct value of a non-perfect square
Students need to simplify the numbers inside the square root, ensuring they identify the approximate value correctly.
For example: √50 = 7 is wrong; the correct answer is √50 ≈ 7.071.
Mistake 4
Confusing the square root symbol with the cube root
Students need to understand the difference between cube root and square root to 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. Students may skip a step accidentally, leading to a wrong answer. This may occur during subtraction or elsewhere in the process.
Square root of 831 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √831?
The area of the square is approximately 831 square units.
Explanation
The area of the square = side^2.
The side length is given as √831.
Area of the square = side^2 = √831 x √831 = 831.
Therefore, the area of the square box is approximately 831 square units.
Problem 2
A square-shaped building measuring 831 square feet is built; if each of the sides is √831, what will be the square feet of half of the building?
415.5 square feet
Explanation
We can just divide the given area by 2 since the building is square-shaped.
Dividing 831 by 2, we get 415.5.
So half of the building measures 415.5 square feet.
Problem 3
Calculate √831 x 5.
144.135
Explanation
The first step is to find the square root of 831, which is approximately 28.83.
The second step is to multiply 28.83 by 5.
So, 28.83 x 5 ≈ 144.135.
Problem 4
What will be the square root of (831 + 9)?
The square root is approximately 30.
Explanation
To find the square root, we need to find the sum of (831 + 9). 831 + 9 = 840, and then √840 ≈ 28.98.
Therefore, the square root of (831 + 9) is approximately 29.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √831 units and the width ‘w’ is 40 units.
The perimeter of the rectangle is approximately 137.66 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√831 + 40) = 2 × (28.83 + 40) = 2 × 68.83 = 137.66 units.
FAQ on Square Root of 831
1.What is √831 in its simplest form?
2.Mention the factors of 831.
3.Calculate the square of 831.
4.Is 831 a prime number?
5.831 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 831?
8.How do technology and digital tools in Singapore support learning Algebra and Square Root of 831?
9.Does learning Algebra support future career opportunities for students in Singapore?
Important Glossaries for the Square Root of 831
- Square root: A square root is the inverse operation of squaring a number. For example, 4^2 = 16, and the inverse of squaring is finding the square root: √16 = 4.
- Irrational number: An irrational number cannot be expressed as a simple fraction; it has an infinite and non-repeating decimal expansion.
- Principal square root: A number has both positive and negative square roots; however, the positive square root is commonly used, known as the principal square root.
- Approximation: The process of finding a value that is close to the actual value, often used when the exact value is difficult or impossible to determine.
- Divisor: A number by which another number is to be divided.
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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.
