Last updated on May 26th, 2025
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 fields like vehicle design, finance, etc. Here, we will discuss the square root of 2448.
The square root is the inverse of squaring a number. 2448 is not a perfect square. The square root of 2448 is expressed in both radical and exponential form. In radical form, it is expressed as √2448, whereas in exponential form it is (2448)^(1/2). √2448 ≈ 49.478, which is an irrational number because it cannot 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. However, for non-perfect square numbers, the prime factorization method is not used; instead, 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 2448 is broken down into its prime factors.
Step 1: Finding the prime factors of 2448 Breaking it down, we get 2 × 2 × 2 × 2 × 3 × 3 × 17: 2^4 × 3^2 × 17
Step 2: Now we have found the prime factors of 2448. The next step is to make pairs of those prime factors. Since 2448 is not a perfect square, the digits of the number can’t be grouped in pairs perfectly. Therefore, calculating √2448 using prime factorization alone is not straightforward.
The long division method is particularly used for non-perfect square numbers. In this method, we check the closest perfect square number for the given number. 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 2448, we group it as 48 and 24.
Step 2: Now we need to find a number n whose square is less than or equal to 24. We can start with n as 4 because 4 × 4 = 16, which is less than 24. The quotient is 4, and after subtracting 16 from 24, the remainder is 8.
Step 3: Bring down 48, the new dividend. Add the old divisor with the same number, 4 + 4 = 8, which will be part of our new divisor.
Step 4: The new divisor will be 80 + x, where x is to be determined. We need to find x such that 80x × x ≤ 848.
Step 5: If we try x = 1, then 81 × 1 = 81, which is too small. Trying x = 9, 89 × 9 = 801, which is suitable.
Step 6: Subtract 801 from 848, the remainder is 47, and the quotient is 49.
Step 7: Since the dividend is less than the divisor, we add a decimal point. Adding the decimal point allows us to add two zeroes to the dividend. Now the new dividend is 4700.
Step 8: Now we need to find the new divisor that is 989 because 989 × 4 = 3956.
Step 9: Subtract 3956 from 4700 to get the remainder 744.
Step 10: The quotient is now 49.4.
Step 11: Continue these steps until we get two numbers after the decimal point or until the remainder is zero.
So the square root of √2448 is approximately 49.48.
The approximation method is another way to find square roots. It is an easy method to find the square root of a given number. Let us learn how to find the square root of 2448 using the approximation method.
Step 1: Identify the closest perfect squares around 2448. The nearest perfect squares are 2401 (49^2) and 2500 (50^2). √2448 falls between 49 and 50.
Step 2: Use the approximation formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square).
Using the formula (2448 - 2401) / (2500 - 2401) = 47 / 99 ≈ 0.4747.
Adding this decimal to the integer part: 49 + 0.4747 = 49.4747.
So, the square root of 2448 is approximately 49.48.
Students often make mistakes while finding the square root, such as forgetting about the negative square root or skipping steps in the long division method. Let's look at some common mistakes and how to avoid them.
Can you help Max find the area of a square box if its side length is given as √2448?
The area of the square box is approximately 2448 square units.
The area of the square = side^2.
The side length is given as √2448.
Area of the square = √2448 × √2448 = 2448.
Therefore, the area of the square box is approximately 2448 square units.
A square-shaped building measuring 2448 square feet is built; if each of the sides is √2448, what will be the square feet of half of the building?
1224 square feet
Since the building is square-shaped, we divide the total area by 2 to find half of it.
Dividing 2448 by 2 gives us 1224.
So, half of the building measures 1224 square feet.
Calculate √2448 × 5.
Approximately 247.39
First, find the square root of 2448, which is approximately 49.48.
Then multiply 49.48 by 5.
So, 49.48 × 5 ≈ 247.39.
What will be the square root of (2448 + 2)?
The square root is approximately 50.
To find the square root, first sum (2448 + 2) = 2450.
Then find √2450 ≈ 50.
Therefore, the square root of (2448 + 2) is approximately ±50.
Find the perimeter of the rectangle if its length 'l' is √2448 units and the width 'w' is 38 units.
The perimeter of the rectangle is approximately 174.96 units.
The perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√2448 + 38) ≈ 2 × (49.48 + 38) ≈ 2 × 87.48 = 174.96 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.
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