Last updated on May 26th, 2025
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.
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.
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:
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.
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.
Students often make mistakes while calculating square roots, such as ignoring the negative root or misapplying methods. Let's address some common errors.
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.
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.
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
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.
Calculate √460 x 3.
64.3428
First, find the approximate square root of 460, which is 21.447.
Multiply this by 3: 21.447 x 3 = 64.3428
What will be the square root of (460 + 16)?
The square root is 22.
First, find the sum of (460 + 16): 460 + 16 = 476, and then √476 = 21.817, approximately equal to 22.
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.
Perimeter of a rectangle = 2 × (length + width)
Perimeter = 2 × (√460 + 40) = 2 × (21.447 + 40) = 2 × 61.447 = 122.894 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.