128 LearnersLast updated on May 26th, 2025
Square Root of 460
If a number is multiplied by itself, the result is a square. The inverse operation is finding the square root. The square root is used in fields such as engineering, physics, and computer science. Here, we will discuss the square root of 460.
What is the Square Root of 460?
The square root is the inverse operation of squaring a number. Since 460 is not a perfect square, its square root cannot be expressed as an integer. The square root of 460 is expressed in both radical and exponential forms. In radical form, it is expressed as √460, whereas in exponential form, it is (460)^(1/2). The approximate value of √460 is 21.4476, which is an irrational number because it cannot be expressed as a simple fraction.
Finding the Square Root of 460
The prime factorization method is typically used for perfect square numbers. For non-perfect squares like 460, the long division and approximation methods are more appropriate. Let's explore these methods:
- Long division method
- Approximation method
Square Root of 460 by Long Division Method
The long division method is useful for non-perfect squares. Here's how we find the square root of 460 using this method:
Step 1: Group the digits of 460 from right to left as 60 and 4.
Step 2: Find the largest number n whose square is less than or equal to 4. Here, n is 2 because 2 x 2 = 4. Subtract to get a remainder of 0.
Step 3: Bring down 60, making it the new dividend. Double the divisor (2), resulting in 4.
Step 4: Find the next digit of the quotient. We try n such that (4n) x n ≤ 60. Let n = 1, giving 41 x 1 = 41. Subtract to get a remainder of 19.
Step 5: Add a decimal point to the quotient and bring down 00, making the new dividend 1900.
Step 6: Double the quotient 21 to get 42. Find n such that (420 + n) x n ≤ 1900. Let n = 4, giving 424 x 4 = 1696. Subtract to get 204.
Step 7: Continue this process to achieve the desired precision.
The square root of 460 is approximately 21.447.
Square Root of 460 by Approximation Method
The approximation method provides a quick way to estimate square roots. Here's how to find the square root of 460 using approximation:
Step 1: Identify the closest perfect squares around 460. The perfect squares are 441 (21²) and 484 (22²). Thus, √460 lies between 21 and 22.
Step 2: Apply the formula: (Given number - smaller perfect square) / (larger perfect square - smaller perfect square) (460 - 441) / (484 - 441) = 19 / 43 ≈ 0.442
Step 3: Add this decimal to the smaller square root: 21 + 0.442 = 21.442
Therefore, the square root of 460 is approximately 21.442.
Common Mistakes and How to Avoid Them in the Square Root of 460
Students often make mistakes while calculating square roots, such as ignoring the negative root or misapplying methods. Let's address some common errors.
Mistake 1
Ignoring the Negative Square Root
It's essential to remember that every positive number has both a positive and negative square root. However, we often use only the positive root for practical applications.
For example, √50 = ±7.07, but the negative root is often overlooked.
Mistake 2
Incorrect Placement of the Square Root Symbol
A common error is misplacing the square root symbol. It's crucial to simplify inside the square root before proceeding.
Example: √(12 + 24) ≠ √12 + √24. The correct method is √(12 + 24) = √36.
Mistake 3
Misestimating Non-Perfect Square Values
Students might incorrectly estimate non-perfect squares if they don't accurately simplify the expression inside the root.
Example: √50 ≠ 7; the correct value is approximately 7.071.
Mistake 4
Confusing Square and Cube Roots
Distinguish between square and cube roots, as they have different operations. For example, √50 and ∛50 are not the same. Emphasize the difference in classroom discussions.
Mistake 5
Errors in Long Division Steps
The long division method can be complex, leading to skipped steps or calculation errors. Ensure each step is followed precisely to avoid mistakes.
Square Root of 460 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √460?
The area of the square is 460 square units.
Explanation
The area of the square = side².
The side length is given as √460.
Area of the square = (√460)² = 460
Therefore, the area of the square box is 460 square units.
Problem 2
A square-shaped garden has an area of 460 square feet. If each side is √460 feet, what is the area of half of the garden?
230 square feet
Explanation
To find the area of half the garden, divide the total area by 2. 460 / 2 = 230
So half of the garden measures 230 square feet.
Problem 3
Calculate √460 x 3.
64.3428
Explanation
First, find the approximate square root of 460, which is 21.447.
Multiply this by 3: 21.447 x 3 = 64.3428
Problem 4
What will be the square root of (460 + 16)?
The square root is 22.
Explanation
First, find the sum of (460 + 16): 460 + 16 = 476, and then √476 = 21.817, approximately equal to 22.
Problem 5
Find the perimeter of a rectangle if its length ‘l’ is √460 units and the width ‘w’ is 40 units.
The perimeter of the rectangle is 122.894 units.
Explanation
Perimeter of a rectangle = 2 × (length + width)
Perimeter = 2 × (√460 + 40) = 2 × (21.447 + 40) = 2 × 61.447 = 122.894 units.
FAQ on Square Root of 460
1.What is √460 in its simplest form?
2.Mention the factors of 460.
3.Calculate the square of 460.
4.Is 460 a prime number?
5.460 is divisible by?
6.How does learning Algebra help students in Indonesia make better decisions in daily life?
7.How can cultural or local activities in Indonesia support learning Algebra topics such as Square Root of 460?
8.How do technology and digital tools in Indonesia support learning Algebra and Square Root of 460?
9.Does learning Algebra support future career opportunities for students in Indonesia?
Important Glossaries for the Square Root of 460
- Square root: A square root is the inverse operation of squaring a number. Example: 5² = 25, and the inverse operation is √25 = 5.
- Irrational number: An irrational number cannot be expressed as a fraction of two integers. Examples include √2, √3, and π.
- Long division method: A technique for finding the square root of non-perfect squares by dividing and averaging.
- Approximation method: A method to estimate square roots by locating the closest perfect squares.
- Perfect square: A number that is the square of an integer. Examples include 1, 4, 9, 16, 25, etc.
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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.
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