119 LearnersLast updated on May 26th, 2025
Square Root of 683
If a number is multiplied by itself, the result is a square. The inverse of this process is finding the square root. Square roots are used in fields like vehicle design, finance, etc. Here, we will discuss the square root of 683.
What is the Square Root of 683?
The square root is the inverse of squaring a number. 683 is not a perfect square. The square root of 683 can be expressed in both radical and exponential forms. In radical form, it is expressed as √683, whereas in exponential form, it is (683)¹/². √683 ≈ 26.1108, which is an irrational number because it cannot be expressed as a ratio p/q, where p and q are integers and q ≠ 0.
Finding the Square Root of 683
The prime factorization method is suitable for perfect square numbers. However, for non-perfect squares like 683, methods like long division or approximation are used. Let's explore these methods:
- Prime factorization method
- Long division method
- Approximation method
Square Root of 683 by Prime Factorization Method
The prime factorization of a number is the product of its prime factors. Let's see how 683 is broken down into its prime factors.
Step 1: Finding the prime factors of 683 683 is a prime number itself, having no factors other than 1 and 683. Therefore, the prime factorization method is not applicable for finding its square root.
Square Root of 683 by Long Division Method
The long division method is particularly used for non-perfect square numbers. Let's learn how to find the square root using this method, step by step.
Step 1: Group the numbers from right to left. For 683, we consider 683 as a single group.
Step 2: Find the largest number whose square is less than or equal to 683. This number is 26, since 26² = 676, which is less than 683.
Step 3: Subtract 676 from 683, leaving a remainder of 7.
Step 4: Bring down pairs of zeros to the right of the remainder.
Step 5: Double the divisor (26) to get 52, and find a digit x such that 52x * x is less than or equal to 700. Here, x = 1 works, as 521 * 1 = 521.
Step 6: Subtract 521 from 700, leaving 179.
Step 7: Bring down another pair of zeros, making it 17900.
Step 8: Continue the division process to get the desired precision. Thus, √683 ≈ 26.11.
Square Root of 683 by Approximation Method
The approximation method is a simpler way to find square roots. Let's use it to find the square root of 683.
Step 1: Identify the perfect squares closest to 683. The perfect squares are 676 (26²) and 729 (27²). Thus, √683 is between 26 and 27.
Step 2: Use linear interpolation: (683 - 676) / (729 - 676) = 7 / 53 ≈ 0.132
So, √683 ≈ 26 + 0.132 = 26.132
Common Mistakes and How to Avoid Them in the Square Root of 683
Students often make mistakes while finding square roots, such as ignoring negative roots or skipping steps in the long division method. Let's explore common mistakes in detail.
Mistake 1
Forgetting about the Negative Square Root
It's important to remember that a number has both positive and negative square roots. However, we often focus on the positive square root due to its practical applications.
For example, √50 = 7.07, but there's also -7.07.
Mistake 2
Not Adding the Square Root Symbol Properly
Incorrect use of the square root symbol is common. Teach students to simplify numbers under the square root before moving on.
For example, √(12 + 24) ≠ √12 + √24. The correct approach is √(12 + 24) = √36.
Mistake 3
Not Finding the Correct Value of a Non-Perfect Square
Simplifying numbers under the square root is crucial to avoid errors in identifying approximate values.
For example, √50 ≠ 7; the correct value is √50 ≈ 7.071.
Mistake 4
Confusing the Square Root Symbol with the Cube Root
It's important to differentiate between square and cube roots to avoid mistakes.
For example, √50 and ∛50 are different.
Mistake 5
Making Mistakes in Long Division
The long division method involves multiple steps, and students might skip a step accidentally, leading to incorrect results. This can happen during subtraction or elsewhere in the process.
Square Root of 683 Examples
Problem 1
Can you help Max find the area of a square if its side length is given as √683?
The area of the square is approximately 683 square units.
Explanation
The area of a square is side².
Given the side length is √683
Area = (√683)² = 683 square units.
Problem 2
A square-shaped building measuring 683 square feet is built; if each of the sides is √683, what will be the square feet of half of the building?
341.5 square feet
Explanation
For a square-shaped building, dividing the total area by 2 gives the area of half the building.
683 / 2 = 341.5 square feet
Problem 3
Calculate √683 x 5.
Approximately 130.554
Explanation
First, find the square root of 683, which is approximately 26.1108.
Then multiply by 5: 26.1108 x 5 ≈ 130.554
Problem 4
What will be the square root of (683 + 17)?
The square root is approximately 26.419
Explanation
First, find the sum of 683 + 17 = 700.
Then, find the square root of 700, which is approximately 26.419.
Problem 5
Find the perimeter of a rectangle if its length ‘l’ is √683 units and the width ‘w’ is 38 units.
The perimeter of the rectangle is approximately 128.2216 units.
Explanation
Perimeter of a rectangle = 2 × (length + width)
Perimeter = 2 × (√683 + 38) = 2 × (26.1108 + 38) ≈ 2 × 64.1108 = 128.2216 units.
FAQ on Square Root of 683
1.What is √683 in its simplest form?
2.Is 683 a Prime Number?
3.Calculate the square of 683.
4.What are the factors of 683?
5.Is 683 divisible by any number other than 1 and itself?
6.How does learning Algebra help students in Bahrain make better decisions in daily life?
7.How can cultural or local activities in Bahrain support learning Algebra topics such as Square Root of 683?
8.How do technology and digital tools in Bahrain support learning Algebra and Square Root of 683?
9.Does learning Algebra support future career opportunities for students in Bahrain?
Important Glossaries for the Square Root of 683
- Square root: The square root is the inverse operation of squaring a number. For example, 4² = 16, and the square root of 16 is √16 = 4.
- Irrational number: An irrational number cannot be expressed as a simple fraction p/q, where p and q are integers, and q ≠ 0.
- Prime number: A prime number is a number greater than 1 that has no divisors other than 1 and itself.
- Linear interpolation: A method used to estimate values between two known values on a line or curve.
- Long division method: A step-by-step method used to divide numbers and find square roots, especially useful for non-perfect squares.
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About BrightChamps in Bahrain
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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