137 LearnersLast updated on May 26th, 2025
Square Root of 2916
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 2916.
What is the Square Root of 2916?
The square root is the inverse of the square of the number. 2916 is a perfect square. The square root of 2916 is expressed in both radical and exponential form. In radical form, it is expressed as √2916, whereas (2916)^(1/2) in exponential form. √2916 = 54, 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 2916
The prime factorization method is used for perfect square numbers. Let us now learn the following methods:
- Prime factorization method
- Long division method
- Approximation method
Square Root of 2916 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 2916 is broken down into its prime factors:
Step 1: Finding the prime factors of 2916 Breaking it down, we get 2 x 2 x 3 x 3 x 3 x 3 x 3 x 3: 2^2 x 3^6
Step 2: Now we found out the prime factors of 2916. The second step is to make pairs of those prime factors. Since 2916 is a perfect square, therefore, the digits of the number can be grouped in pairs to get: √2916 = (2 x 3^3) = 54
Square Root of 2916 by Long Division Method
The long division method is also used for finding the square root of numbers. 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 2916, we need to group it as 29 and 16.
Step 2: Now, we need to find n whose square is less than or equal to 29. We can say n as 5, because 5 x 5 = 25. Now the quotient is 5. After subtracting 25 from 29, the remainder is 4.
Step 3: Bring down 16 to make the new dividend 416. Add the old divisor with the same number 5 + 5 to get 10, which will be our new divisor.
Step 4: The new divisor is 10n. We need to find the value of n such that 10n x n is less than or equal to 416. Let n be 4, then 104 x 4 = 416. Step 5: Subtracting 416 from 416, we get the remainder 0.
The quotient is 54. So, the square root of √2916 is 54.
Square Root of 2916 by Approximation Method
Approximation method is another method for finding the 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 2916 using the approximation method. Since 2916 is a perfect square, it lies exactly between the perfect squares of 2809 (53^2) and 3025 (55^2). Therefore, √2916 = 54.
Common Mistakes and How to Avoid Them in the Square Root of 2916
Students do make mistakes while finding the square root, such as forgetting about the negative square root or skipping steps in long division. Now let us look at a few of those mistakes that students tend to make in detail.
Mistake 1
Forgetting about the negative square root
It is important to make students aware that a number does have both positive and negative square roots. However, we usually take only the positive square root, as it is the required one.
For example: √49 = 7, there is also -7 which should not be forgotten.
Mistake 2
Not adding the square root symbol in proper places
Not using the square root properly is another mistake that children make. To resolve this, we need to teach children that simplifying the numbers inside the square root is important and then move on to the second step.
For example: √(16 + 9) = √16 + √9 is the wrong method of using roots. The right way of using roots is √(16 + 9) = √25 = 5.
Mistake 3
Not finding the correct value of a non-perfect square
The first step that needs to be taught to children is to simplify the numbers inside the square root correctly. This is important so that students do not make mistakes while identifying the approximate value.
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 be taught the difference between cube root and square root constantly, as this will help them avoid mistakes.
For example: √64 and ∛64 are different.
Mistake 5
Making mistakes in long division
Finding a square root using the long division method involves many steps. Due to this, many students might skip a step accidentally, which results in a wrong answer at the end of the sum. This may either happen in subtracting or elsewhere.
Square Root of 2916 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √2916?
The area of the square is 2916 square units.
Explanation
The area of the square = side^2.
The side length is given as √2916.
Area of the square = side^2 = √2916 x √2916 = 54 x 54 = 2916.
Therefore, the area of the square box is 2916 square units.
Problem 2
A square-shaped building measuring 2916 square feet is built; if each of the sides is √2916, what will be the square feet of half of the building?
1458 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 2916 by 2, we get 1458.
So, half of the building measures 1458 square feet.
Problem 3
Calculate √2916 x 5.
270
Explanation
The first step is to find the square root of 2916, which is 54.
The second step is to multiply 54 by 5.
So, 54 x 5 = 270.
Problem 4
What will be the square root of (2916 + 84)?
The square root is 55.
Explanation
To find the square root, we need to find the sum of (2916 + 84).
2916 + 84 = 3000, and then √3000 ≈ 54.77.
For simplicity in this context, we're considering the nearest whole number, which is 55.
Therefore, the square root of (2916 + 84) is approximately ±55.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √2916 units and the width ‘w’ is 20 units.
We find the perimeter of the rectangle as 148 units.
Explanation
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√2916 + 20)
= 2 × (54 + 20)
= 2 × 74
= 148 units.
FAQ on Square Root of 2916
1.What is √2916 in its simplest form?
2.Mention the factors of 2916.
3.Calculate the square of 2916.
4.Is 2916 a prime number?
5.2916 is divisible by?
6.How does learning Algebra help students in United Arab Emirates make better decisions in daily life?
7.How can cultural or local activities in United Arab Emirates support learning Algebra topics such as Square Root of 2916?
8.How do technology and digital tools in United Arab Emirates support learning Algebra and Square Root of 2916?
9.Does learning Algebra support future career opportunities for students in United Arab Emirates?
Important Glossaries for the Square Root of 2916
- Square root: A square root is the inverse of a square. Example: 7^2 = 49, and the inverse of the square is the square root, that is √49 = 7.
- Rational number: A rational number is a number that can be written in the form of p/q, where q is not equal to zero and p and q are integers.
- Perfect square: A perfect square is an integer that is the square of an integer. For example, 36 is a perfect square because it is 6^2.
- Prime factorization: The expression of a number as the product of its prime factors. For example, the prime factorization of 12 is 2^2 x 3.
- Long division method: A step-by-step process of dividing numbers to find the square root by grouping and dividing the digits systematically.
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About BrightChamps in United Arab Emirates
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.
