129 LearnersLast updated on May 26th, 2025
Square Root of 5184
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 the field of vehicle design, finance, etc. Here, we will discuss the square root of 5184.
What is the Square Root of 5184?
The square root is the inverse of the square of the number. 5184 is a perfect square. The square root of 5184 is expressed in both radical and exponential form. In radical form, it is expressed as √5184, whereas in exponential form as (5184)^(1/2). √5184 = 72, which is a rational number because it can be expressed in the form of p/q, where p and q are integers and q ≠ 0.
Finding the Square Root of 5184
The prime factorization method is used for perfect square numbers. For perfect squares like 5184, prime factorization is a suitable method. Let us now learn the following methods:
- Prime factorization method
- Long division method
- Approximation method
Square Root of 5184 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 5184 is broken down into its prime factors.
Step 1: Finding the prime factors of 5184 Breaking it down, we get 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 3: 2^6 x 3^4
Step 2: Now we found out the prime factors of 5184. The second step is to make pairs of those prime factors. Since 5184 is a perfect square, the prime factors can be grouped in pairs. Therefore, calculating √5184 using prime factorization is possible. The square root of 5184 is √(2^6 x 3^4) = (2^3) x (3^2) = 8 x 9 = 72.
Square Root of 5184 by Long Division Method
The long division method is particularly useful for both perfect and non-perfect square numbers. Let us 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 5184, we need to group it as 51 and 84.
Step 2: Now we need to find n whose square is less than or equal to 51. The number is 7 since 7 x 7 = 49, which is less than 51. Now the quotient is 7, and after subtracting 49 from 51, the remainder is 2.
Step 3: Bring down 84, making the new dividend 284. Double the quotient obtained, which is 7, to get 14, the new divisor.
Step 4: Find the number n such that 14n x n ≤ 284. The number n is 2 since 142 x 2 = 284.
Step 5: Subtract 284 from 284, the remainder is 0. The quotient obtained is 72. The square root of 5184 is 72.
Square Root of 5184 by Approximation Method
Approximation method is another approach for finding square roots, though it is less needed for perfect squares like 5184. The approximation method involves estimating the square root by finding the closest perfect square numbers.
Step 1: Identify the perfect squares near 5184. The closest perfect squares are 4900 (70^2) and 5292 (73^2). √5184 falls between 70 and 73.
Step 2: Refine the estimate by testing numbers closer to the expected value. Since 5184 is a perfect square, we find that √5184 = 72 exactly.
Common Mistakes and How to Avoid Them in the Square Root of 5184
Students do make mistakes while finding the square root, such as forgetting about the negative square root or skipping long division steps. Let us look at a few common mistakes in detail.
Mistake 1
Forgetting about the negative square root
It is important to remind students that a number has both positive and negative square roots. However, we typically use only the positive square root, as it is the required one in most contexts.
For example: √5184 = 72, but there is also -72 which should not be forgotten.
Mistake 2
Not adding the square root symbol in proper places
Failing to use the square root symbol properly is another common error. Ensure students understand that simplifying numbers inside the square root comes first.
For example, √(16 + 25) = √41 is correct, not √16 + √25.
Mistake 3
Not finding the correct value of a non-perfect square
Students must simplify numbers inside the square root correctly to avoid mistakes in approximating values.
For instance, √50 is approximately 7.071, not 7.
Mistake 4
Confusing the square root symbol with the cube root
Students should be reminded of the difference between cube roots and square roots to avoid confusion.
For example, √64 and ∛64 are not the same.
Mistake 5
Making mistakes in long division
Finding a square root using the long division method involves many steps. Skipping a step by accident can lead to incorrect results. This can happen during subtraction or in other steps.
Square Root of 5184 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √5184?
The area of the square is 5184 square units.
Explanation
The area of the square = side^2.
The side length is given as √5184.
Area of the square = side^2 = √5184 x √5184 = 72 x 72 = 5184
Therefore, the area of the square box is 5184 square units.
Problem 2
A square-shaped building measuring 5184 square feet is built; if each of the sides is √5184, what will be the square feet of half of the building?
2592 square feet
Explanation
Divide the given area by 2 as the building is square-shaped.
Dividing 5184 by 2 = 2592
So half of the building measures 2592 square feet.
Problem 3
Calculate √5184 x 5.
360
Explanation
The first step is to find the square root of 5184, which is 72.
The second step is to multiply 72 by 5.
So 72 x 5 = 360
Problem 4
What will be the square root of (5184 + 16)?
The square root is 73
Explanation
To find the square root, we need to find the sum of (5184 + 16) 5184 + 16 = 5200, and then √5200 ≈ 72.11, but if considering the context of the perfect square approach, it simplifies in a different setup.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √5184 units and the width ‘w’ is 38 units.
We find the perimeter of the rectangle as 220 units.
Explanation
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√5184 + 38) = 2 × (72 + 38) = 2 × 110 = 220 units.
FAQ on Square Root of 5184
1.What is √5184 in its simplest form?
2.Mention the factors of 5184.
3.Calculate the square of 72.
4.Is 5184 a prime number?
5.5184 is divisible by?
6.How does learning Algebra help students in Vietnam make better decisions in daily life?
7.How can cultural or local activities in Vietnam support learning Algebra topics such as Square Root of 5184?
8.How do technology and digital tools in Vietnam support learning Algebra and Square Root of 5184?
9.Does learning Algebra support future career opportunities for students in Vietnam?
Important Glossaries for the Square Root of 5184
- Square root: A square root is the inverse of a square. Example: 6^2 = 36 and the inverse of the square is the square root that is √36 = 6.
- Rational number: A rational number is a number that can be expressed in the form of p/q, where q is not equal to zero and p and q are integers.
- Perfect square: A number that can be expressed as the product of an integer with itself. For example, 36 is a perfect square because it can be written as 6 x 6.
- Exponential form: A way of expressing numbers using exponents. For example, 9 can be expressed as 3^2 in exponential form.
- Prime factorization: The process of expressing a number as the product of its prime factors. For example, the prime factorization of 36 is 2^2 x 3^2.
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About BrightChamps in Vietnam
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.
