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Last updated on May 26th, 2025

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Square Root of 460

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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.

Square Root of 460 for Indonesian Students
Professor Greenline from BrightChamps

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.

Professor Greenline from BrightChamps

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
Professor Greenline from BrightChamps

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.

Professor Greenline from BrightChamps

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.

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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

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Ignoring the Negative Square Root

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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.

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Square Root of 460 Examples

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Max, the Girl Character from BrightChamps

Problem 1

Can you help Max find the area of a square box if its side length is given as √460?

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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.

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Max, the Girl Character from BrightChamps

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?

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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.

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Max, the Girl Character from BrightChamps

Problem 3

Calculate √460 x 3.

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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

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Max, the Girl Character from BrightChamps

Problem 4

What will be the square root of (460 + 16)?

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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.

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Max, the Girl Character from BrightChamps

Problem 5

Find the perimeter of a rectangle if its length ‘l’ is √460 units and the width ‘w’ is 40 units.

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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.

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FAQ on Square Root of 460

1.What is √460 in its simplest form?

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2.Mention the factors of 460.

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3.Calculate the square of 460.

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4.Is 460 a prime number?

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5.460 is divisible by?

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6.How does learning Algebra help students in Indonesia make better decisions in daily life?

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7.How can cultural or local activities in Indonesia support learning Algebra topics such as Square Root of 460?

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8.How do technology and digital tools in Indonesia support learning Algebra and Square Root of 460?

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9.Does learning Algebra support future career opportunities for students in Indonesia?

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Professor Greenline from BrightChamps

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.
Professor Greenline from BrightChamps

About BrightChamps in Indonesia

At BrightChamps, we believe algebra is more than symbols—it’s a doorway to endless possibilities! We aim to help children throughout Indonesia master key math skills, focusing today on the Square Root of 460 with a special emphasis on square roots—in a way that’s fun, lively, and easy to understand. Whether your child is measuring the speed of a roller coaster at Dunia Fantasi, tracking scores in badminton matches, or managing their allowance for the latest gadgets, mastering algebra builds the confidence they need for everyday problems. Our hands-on lessons make learning simple and enjoyable. Because children in Indonesia learn differently, we tailor our approach to fit each learner’s needs. From Jakarta’s bustling streets to Bali’s scenic beaches, BrightChamps brings math to life, making it relevant and exciting across Indonesia. Let’s make square roots a fun part of every child’s math journey!
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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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Max, the Girl Character from BrightChamps

Fun Fact

: He loves to play the quiz with kids through algebra to make kids love it.

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