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 the fields of vehicle design, finance, etc. Here, we will discuss the square root of 2285.
The square root is the inverse of the square of a number. 2285 is not a perfect square. The square root of 2285 is expressed in both radical and exponential forms. In the radical form, it is expressed as √2285, whereas (2285)^(1/2) in the exponential form. √2285 ≈ 47.798, 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, the prime factorization method is not used for non-perfect square numbers where the long-division method and approximation method 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 2285 is broken down into its prime factors.
Step 1: Finding the prime factors of 2285 Breaking it down, we get 5 x 457. The factorization of 457 is 457 itself as it is a prime number.
Step 2: Since 2285 is not a perfect square, the digits of the number can’t be grouped in pairs.
Therefore, calculating √2285 using prime factorization alone is not feasible.
The long division method is particularly used for non-perfect square numbers. In this method, we should 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: Start by grouping the digits from right to left. For 2285, group it as 22 and 85.
Step 2: Find a number whose square is less than or equal to 22. This is 4, as 4 x 4 = 16. Subtract 16 from 22 to get 6, and bring down the next pair 85, making it 685.
Step 3: Double the divisor (4), getting 8, and find a digit n such that 8n x n is less than or equal to 685.
Step 4: Find n = 7, as 87 x 7 = 609. Subtract 609 from 685 to get 76.
Step 5: Add a decimal point and bring down 00 to make it 7600. Repeat the process.
Step 6: Continue the long division process to get a more accurate value.
The approximation method is another method for finding 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 2285 using the approximation method.
Step 1: Find the closest perfect squares to 2285. 2025 (45²) and 2304 (48²) are the closest. √2285 falls between 45 and 48.
Step 2: Use interpolation to find the approximate value: (2285 - 2025) / (2304 - 2025) = (260 / 279).
This shows that √2285 is approximately midway, yielding an answer around 47.8.
Students do make mistakes while finding the square root, such as forgetting about the negative square root, skipping long division methods, etc. 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 √2285?
The area of the square is approximately 5228.04 square units.
The area of the square = side².
The side length is given as √2285.
Area of the square = side² = √2285 × √2285 ≈ 47.798 × 47.798 ≈ 2285.
Therefore, the area of the square box is approximately 5228.04 square units.
A square-shaped building measuring 2285 square feet is built; if each of the sides is √2285, what will be the square feet of half of the building?
1142.5 square feet
We can simply divide the given area by 2 as the building is square-shaped. Dividing 2285 by 2 = 1142.5
Calculate √2285 × 5.
Approximately 238.99
The first step is to find the square root of 2285, which is approximately 47.798, and then multiply 47.798 by 5.
So, 47.798 × 5 ≈ 238.99
What will be the square root of (2280 + 5)?
The square root is approximately 47.798
To find the square root, we need to find the sum of (2280 + 5), which is 2285.
The square root of 2285 is approximately 47.798.
Find the perimeter of a rectangle if its length ‘l’ is √2285 units and the width ‘w’ is 38 units.
We find the perimeter of the rectangle as approximately 171.596 units.
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√2285 + 38) ≈ 2 × (47.798 + 38) ≈ 2 × 85.798 ≈ 171.596 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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