117 LearnersLast updated on May 26th, 2025
Square Root of 2304
If a number is multiplied by itself, the result is a square. The inverse of the square is a square root. The square root is used in fields like vehicle design, finance, etc. Here, we will discuss the square root of 2304.
What is the Square Root of 2304?
The square root is the inverse of the square of the number. 2304 is a perfect square. The square root of 2304 is expressed in both radical and exponential form. In radical form, it is expressed as √2304, whereas (2304)^(1/2) in exponential form. √2304 = 48, 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 2304
The prime factorization method is used for perfect square numbers. For non-perfect square numbers, the long-division and approximation methods are used. Let us now learn the following methods:
- Prime factorization method
- Long division method
- Approximation method
Square Root of 2304 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 2304 is broken down into its prime factors.
Step 1: Finding the prime factors of 2304 Breaking it down, we get 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 2 x 2: 2^8 x 3^2
Step 2: Now we make pairs of those prime factors. Since 2304 is a perfect square, we can group the digits of the number in pairs.
Therefore, calculating √2304 using prime factorization gives us 48.
Square Root of 2304 by Long Division Method
The long division method is particularly used for both perfect and non-perfect square 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 2304, we group it as 23 and 04.
Step 2: Now, we need to find n whose square is less than or equal to 23. We can say n is '4' because 4 x 4 = 16, which is less than 23. Now the quotient is 4, and after subtracting 16 from 23, the remainder is 7.
Step 3: Now let us bring down 04, making the new dividend 704. Add the old divisor with the quotient 4 + 4 = 8, which will be our new divisor.
Step 4: The new divisor is 8n, and we find n such that 8n x n ≤ 704. Let us consider n as 8, now 88 x 8 = 704.
Step 5: Subtract 704 from 704; the difference is 0, and the quotient is 48.
Step 6: Since the remainder is zero, the square root of √2304 is 48.
Square Root of 2304 by Approximation Method
The approximation method is another technique for finding square roots. It's straightforward to find the square root of a given number. Now let us learn how to find the square root of 2304 using the approximation method.
Step 1: First, we need to find the closest perfect squares around 2304. 2304 is a perfect square itself.
Step 2: Therefore, the square root of 2304 is exactly 48.
Common Mistakes and How to Avoid Them in the Square Root of 2304
Students often make mistakes while finding the square root, such as forgetting about the negative square root or skipping steps in long division methods. 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 has both positive and negative square roots. However, we usually consider only the positive square root in practical scenarios.
Mistake 2
Not adding square root symbol in proper places
Not using the square root properly is another mistake. To resolve this, we need to ensure students simplify the numbers inside the square root before proceeding.
For example: √(12 + 24) ≠ √12 + √24; the correct simplification is √(12 + 24) = √36 = 6.
Mistake 3
Not finding the correct value of a perfect square
The first step that needs to be taught to children is to verify if a number is a perfect square.
For example, √2304 = 48, not 47 or 49.
Mistake 4
Confusing the square root symbol with the cube root
Students need to be taught the difference between cube roots and square roots constantly.
For example, √2304 and ∛2304 are different.
Mistake 5
Making mistakes in long division
Finding a square root using the long division method involves many steps. Many students might skip a step accidentally, resulting in a wrong answer. This may happen in subtraction or elsewhere.
Square Root of 2304 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √2304?
The area of the square is 2304 square units.
Explanation
The area of the square = side².
The side length is given as √2304.
Area of the square = (side)² = √2304 x √2304 = 48 x 48 = 2304.
Therefore, the area of the square box is 2304 square units.
Problem 2
A square-shaped building measuring 2304 square feet is built; if each of the sides is √2304, what will be the square feet of half of the building?
1152 square feet
Explanation
We can simply divide the given area by 2 as the building is square-shaped.
Dividing 2304 by 2 gives us 1152.
So half of the building measures 1152 square feet.
Problem 3
Calculate √2304 x 5.
240
Explanation
The first step is to find the square root of 2304, which is 48.
The second step is to multiply 48 by 5.
So 48 x 5 = 240.
Problem 4
What will be the square root of (2300 + 4)?
The square root is 48
Explanation
To find the square root, we need to find the sum of (2300 + 4).
2300 + 4 = 2304, and then √2304 = 48.
Therefore, the square root of (2300 + 4) is ±48.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √2304 units and the width ‘w’ is 10 units.
We find the perimeter of the rectangle as 116 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√2304 + 10) = 2 × (48 + 10) = 2 × 58 = 116 units.
FAQ on Square Root of 2304
1.What is √2304 in its simplest form?
2.Mention the factors of 2304.
3.Calculate the square of 48.
4.Is 2304 a prime number?
5.2304 is divisible by?
6.How does learning Algebra help students in United States make better decisions in daily life?
7.How can cultural or local activities in United States support learning Algebra topics such as Square Root of 2304?
8.How do technology and digital tools in United States support learning Algebra and Square Root of 2304?
9.Does learning Algebra support future career opportunities for students in United States?
Important Glossaries for the Square Root of 2304
- Square root: A square root is the inverse of squaring a number. Example: 7² = 49 and the inverse of the square is the square root that is √49 = 7.
- Perfect square: A perfect square is an integer that is the square of an integer. Example: 48² = 2304.
- Rational number: A rational number is a number that can be expressed in the form of p/q, q is not equal to zero and p and q are integers.
- Prime factorization: The process of expressing a number as a product of its prime factors.
- Dividend: In division, the dividend is the number being divided. For example, in 2304 ÷ 48 = 48, 2304 is the dividend.
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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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