133 LearnersLast updated on May 26th, 2025
Square Root of 6084
If a number is multiplied by itself, the result is a square. The inverse operation is finding the square root. The square root has applications in fields such as vehicle design, finance, and more. Here, we will discuss the square root of 6084.
What is the Square Root of 6084?
The square root is the inverse operation of squaring a number. 6084 is a perfect square. The square root of 6084 can be expressed in both radical and exponential forms. In radical form, it is expressed as √6084, and in exponential form, it is (6084)^(1/2). The square root of 6084 is 78, which is a rational number because it can be expressed as a fraction where both the numerator and the denominator are integers.
Finding the Square Root of 6084
The prime factorization method is suitable for perfect square numbers. For non-perfect squares, other methods like the long-division and approximation methods are used. Let's explore these methods:
- Prime Factorization Method
- Long Division Method
- Approximation Method
Square Root of 6084 by Prime Factorization Method
The prime factorization of a number involves expressing it as a product of its prime factors. Let's see how 6084 is broken down into its prime factors.
Step 1: Finding the prime factors of 6084. Breaking it down, we get 2 × 2 × 3 × 3 × 13 × 13.
Step 2: We form pairs of prime factors. The pairs are (2, 2), (3, 3), and (13, 13). Step 3: Taking one number from each pair, we get 2 × 3 × 13 = 78.
Therefore, √6084 = 78.
Square Root of 6084 by Long Division Method
The long division method is particularly useful for non-perfect square numbers, but it can be used for perfect squares as well. Let's find the square root of 6084 using the long division method, step by step.
Step 1: Pair the digits of 6084 from right to left, giving us (60)(84).
Step 2: Find the largest number whose square is less than or equal to 60. This number is 7, because 7 × 7 = 49. Subtract 49 from 60, leaving a remainder of 11.
Step 3: Bring down the next pair of digits, 84, to get 1184.
Step 4: Double the quotient obtained (7), giving 14, and use it as the starting point for the new divisor.
Step 5: Find a digit n such that 14n × n is less than or equal to 1184. The number is 8, since 148 × 8 = 1184.
Step 6: Subtract 1184 from 1184, resulting in a remainder of 0.
Thus, the quotient is 78, so the square root of 6084 is 78.
Square Root of 6084 by Approximation Method
The approximation method is useful for estimating the square root of a number. Here's how to find the square root of 6084 using this method.
Step 1: Identify the closest perfect squares around 6084.
The nearest perfect squares are 5776 (76²) and 6400 (80²). √6084 lies between 76 and 80.
Step 2: Since 6084 is a perfect square, we can use the long division or prime factorization method to find the exact square root, which is 78.
Thus, using approximation, √6084 ≈ 78.
Common Mistakes and How to Avoid Them in the Square Root of 6084
Students often make mistakes when finding square roots, such as neglecting the negative square root or misapplying the long division method. Let's explore these mistakes in detail.
Mistake 1
Forgetting about the negative square root
It's important to remember that every positive number has both a positive and a negative square root. However, we generally consider the positive square root in practical applications.
For example, √6084 = 78 also implies -78 as a square root.
Mistake 2
Not adding the square root symbol correctly
Misplacing the square root symbol is a common error. Ensure students understand that the process involves simplifying the expression under the square root before proceeding.
For example, √(16 + 9) ≠ √16 + √9; instead, it equals √25, which is 5.
Mistake 3
Misidentifying perfect squares
A common mistake is misidentifying whether a number is a perfect square. Ensure students verify the factorization to confirm if a number is a perfect square.
For example, √50 is not a perfect square, whereas 6084 is.
Mistake 4
Confusing the square root with the cube root
It's crucial to distinguish between square roots and cube roots.
For example, √27 is not the same as ∛27. Ensure students understand the symbols and their meanings.
Mistake 5
Errors in the long division method
The long division method involves multiple steps, and missing any step can lead to incorrect results. Ensure students practice and follow each step carefully to arrive at the correct square root.
Square root of 6084 Examples
Problem 1
Can you help Max find the area of a square if its side length is √6084?
The area of the square is 6084 square units.
Explanation
The area of a square is given by side².
The side length is √6084, which is 78.
Area = side² = 78 × 78 = 6084.
Therefore, the area of the square is 6084 square units.
Problem 2
A square-shaped garden measures 6084 square feet. What is the length of each side?
Each side of the garden measures 78 feet.
Explanation
To find the side length of the square, calculate the square root of the area. √6084 = 78.
Thus, each side of the garden is 78 feet long.
Problem 3
Calculate √6084 × 5.
390
Explanation
First, find the square root of 6084, which is 78.
Then multiply 78 by 5. 78 × 5 = 390.
So, √6084 × 5 = 390.
Problem 4
What will be the square root of (6084 + 16)?
The square root is 80.
Explanation
First, find the sum of 6084 and 16, which is 6100.
Next, find the square root of 6100.
Since 6100 is not a perfect square, use approximation: it is close to 80².
Thus, √6100 is approximately 80.
Problem 5
Find the perimeter of a rectangle if its length 'l' is √6084 units and the width 'w' is 38 units.
The perimeter of the rectangle is 232 units.
Explanation
Perimeter of a rectangle = 2 × (length + width).
Length = √6084 = 78 units.
Perimeter = 2 × (78 + 38) = 2 × 116 = 232 units.
FAQ on Square Root of 6084
1.What is √6084 in its simplest form?
2.Mention the factors of 6084.
3.Calculate the square of 78.
4.Is 6084 a prime number?
5.What numbers is 6084 divisible by?
6.How does learning Algebra help students in Canada make better decisions in daily life?
7.How can cultural or local activities in Canada support learning Algebra topics such as Square Root of 6084?
8.How do technology and digital tools in Canada support learning Algebra and Square Root of 6084?
9.Does learning Algebra support future career opportunities for students in Canada?
Important Glossaries for the Square Root of 6084
- Square root: The square root of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 16 is 4, since 4 × 4 = 16.
- Rational number: A rational number is a number that can be expressed as the quotient or fraction of two integers, where the denominator is not zero.
- Perfect square: A perfect square is an integer that is the square of an integer. For instance, 6084 is a perfect square because it is 78 squared.
- Prime factorization: Prime factorization is the process of expressing a number as a product of its prime factors. For example, the prime factorization of 6084 is 2 × 2 × 3 × 3 × 13 × 13.
- Long division method: The long division method is a step-by-step approach used to find the square root of a number by dividing it into smaller, manageable parts.
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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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