Last updated on May 26th, 2025
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.
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.
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:
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.
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.
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.
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.
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.
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.
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
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.
Calculate √2304 x 5.
240
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.
What will be the square root of (2300 + 4)?
The square root is 48
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.
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.
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√2304 + 10) = 2 × (48 + 10) = 2 × 58 = 116 units.
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.
: He loves to play the quiz with kids through algebra to make kids love it.