118 LearnersLast updated on May 29th, 2025
Square of 6084
The product of multiplying an integer by itself is the square of a number. Square is used in programming, calculating areas, and so on. In the topic, we will discuss the square of 6084.
What is the Square of 6084
The square of a number is the product of the number itself.
The square of 6084 is the square of the number whose square is 6084.
We write it in math as n² = 6084, where n is the base and 2 is the exponent.
The square of a positive and a negative number is always positive.
For example, 5² = 25; -5² = 25.
The square root of 6084 is 78 because 78 × 78 = 6084.
Square root of 6084 in arithmetic form: √6084 = 78
How to Calculate the Value of Square Root of 6084
The square root of a number is finding the number which, when multiplied by itself, gives the number. These are the common methods used to find the square root of a number.
- By Factorization Method
- Using a Calculator
By the Factorization Method
In this method, we will factorize the number into its prime factors and pair them to find the square root. Let’s find the square root of 6084.
Step 1: Identify the number. Here, the number is 6084
Step 2: Factorize the number into its prime factors 6084 = 2 × 2 × 3 × 3 × 13 × 13
Step 3: Pair the prime factors and find the square root √6084 = 2 × 3 × 13 = 78
Using a Calculator
Using a calculator to find the square root of a number is the easiest method. Let’s learn how to use a calculator to find the square root of 6084.
Step 1: Enter the number in the calculator Enter 6084 in the calculator.
Step 2: Use the square root function or button (√) Press the square root button to find the answer
Here, the square root of 6084 is 78.
Tips and Tricks for the Square Root of 6084
Tips and tricks make it easy for students to understand and learn the square root of a number. To master the square root of a number, these tips and tricks will help students.
- The square root of a perfect square is always a whole number. For example, √144 = 12.
- The square root of an even perfect square is even. For example, √36 = 6.
- The square root of an odd perfect square is odd. For example, √81 = 9.
- If the square of a number is a fraction or a decimal, then the number is not a perfect square. For example, √1.44 = 1.2
- Estimating square roots can be done by finding the nearest perfect squares. For example, √50 is between √49 (7) and √64 (8).
Common Mistakes to Avoid When Calculating the Square Root of 6084
Mistakes are common among kids when doing math, especially when finding the square root of a number. Let’s learn some common mistakes to master finding the square root of a number.
Mistake 1
Calculation errors:
Calculation errors mostly happen when students skip the steps or else by swapping the digits. To avoid it, students should double-check the answer. They can double-check by squaring the solution they found.
For example, the square root of 625 is 25, and the square of 25 is 625.
Solved Examples on Square Root of 6084
Problem 1
Find the length of the square, where the area of the square is 6084 cm².
The area of a square = a² So, the area of a square = 6084 cm² So, the length = √6084 = 78. The length of each side = 78 cm
Explanation
The length of a square is 78 cm.
Because the area is 6084 cm², the length is √6084 = 78.
Problem 2
A rectangular garden has an area of 6084 square feet and one side measuring 78 feet. Find the other side's length.
The area of the rectangle = length × width Here, area = 6084 square feet, length = 78 feet Width = Area / Length = 6084 / 78 = 78 feet
Explanation
To find the other side of the rectangle, divide the area by the known side length.
So, the other side is 78 feet.
Problem 3
Find the area of a circle whose diameter is 78 meters.
The area of the circle = 4,788.51 m²
Explanation
The area of a circle = πr²
Here, diameter = 78, so radius r = 78/2 = 39
Therefore, the area of the circle = π × 39² = 3.14 × 39 × 39 = 4788.51 m².
Problem 4
The perimeter of a square is 312 cm. Find the side length of the square.
The side length of the square is 78 cm.
Explanation
The perimeter of a square = 4a
Here, perimeter = 312 cm
So, 4a = 312 Therefore, a = 312 / 4 = 78.
Problem 5
Find the square of 79.
The square of 79 is 6241.
Explanation
The square of 79 is multiplying 79 by 79.
So, the square = 79 × 79 = 6241.
FAQs on Square Root of 6084
1.What is the square root of 6084?
2.What is the square of 78?
3.Is 6084 a perfect square?
4.How can I verify the square root of 6084?
5.What is the square of 77?
6.How does learning Algebra help students in United Kingdom make better decisions in daily life?
7.How can cultural or local activities in United Kingdom support learning Algebra topics such as Square of 6084?
8.How do technology and digital tools in United Kingdom support learning Algebra and Square of 6084?
9.Does learning Algebra support future career opportunities for students in United Kingdom?
Important Glossaries for Square Root of 6084
- Perfect square: A number that is the square of an integer. For example, 49 is a perfect square of 7.
- Square root: The square root is a value that, when multiplied by itself, gives the original number. For example, the square root of 144 is 12.
- Factorization: The process of breaking down a number into its prime factors. For example, the factorization of 18 is 2 × 3 × 3.
- Prime number: A number that is only divisible by 1 and itself. For example, 2, 3, 5, 7, etc.
- Arithmetic form: A way of expressing a mathematical operation using numbers and symbols, such as 3 × 3 = 9.
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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.
