122 LearnersLast updated on May 26th, 2025
Square Root of 487
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 such as engineering, architecture, and finance. Here, we will discuss the square root of 487.
What is the Square Root of 487?
The square root is the inverse of squaring a number. 487 is not a perfect square. The square root of 487 is expressed in both radical and exponential form. In radical form, it is expressed as √487, whereas in exponential form, it is expressed as (487)^(1/2). √487 ≈ 22.068, 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.
Finding the Square Root of 487
The prime factorization method is used for perfect square numbers. However, for non-perfect square numbers, the long division method and approximation method are used. Let us now learn the following methods:
- Prime factorization method
- Long division method
- Approximation method
Square Root of 487 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now, let us look at how 487 is broken down into its prime factors:
Step 1: Finding the prime factors of 487. 487 is a prime number, so it cannot be broken down further into other prime factors. Thus, it cannot be simplified using the prime factorization method. Calculating the square root of 487 using prime factorization is not feasible.
Square Root of 487 by Long Division Method
The long division method is particularly used for non-perfect square numbers. 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 in pairs. In the case of 487, we have 4 and 87.
Step 2: Find a number n whose square is less than or equal to 4. This number is 2, because 2 × 2 = 4.
Step 3: Subtract 4 from 4, which leaves a remainder of 0, and bring down the next pair, 87.
Step 4: Double the divisor (2) to get 4, and find a new digit (n) such that 4n × n ≤ 87. This digit is 2, because 42 × 2 = 84.
Step 5: Subtract 84 from 87, resulting in a remainder of 3.
Step 6: Since the dividend is less than the divisor, add a decimal point and bring down a pair of zeros to the remainder to make it 300.
Step 7: The new divisor is 44, and find n such that 44n × n ≤ 300. The number is 6, because 446 × 6 = 2676.
Step 8: Subtract 2676 from 3000 to get a remainder of 324.
Step 9: Continue the process to get the desired precision.
So the square root of √487 ≈ 22.068.
Square Root of 487 by Approximation Method
The approximation method is another method for finding square roots. Now let us learn how to find the square root of 487 using the approximation method.
Step 1: Determine the closest perfect squares surrounding √487. The closest perfect squares are 484 (22^2) and 529 (23^2). Thus, √487 lies between 22 and 23.
Step 2: Apply the formula: (Given number - smallest perfect square) ÷ (Greater perfect square - smallest perfect square). Applying the formula: (487 - 484) ÷ (529 - 484) = 3 ÷ 45 ≈ 0.067. Adding this to 22 gives us 22 + 0.067 ≈ 22.067.
Hence, the square root of 487 is approximately 22.067.
Common Mistakes and How to Avoid Them in the Square Root of 487
Students often make mistakes while finding square roots, such as forgetting about the negative square root or skipping important steps in the long division method. Here are a few common mistakes to avoid:
Mistake 1
Forgetting about the negative square root
It is important to remember that a number has both positive and negative square roots. However, typically only the principal (positive) square root is used in practical applications.
For example: √50 = 7.07 and -7.07.
Mistake 2
Not adding square root symbols in proper places
Incorrect use of square root symbols is a common mistake.
For example, √(12 + 24) = √12 + √24 is incorrect. The correct approach is √(12 + 24) = √36.
Mistake 3
Not finding the correct value of a non-perfect square
Simplifying numbers inside the square root is crucial to finding the approximate value.
For example, stating √50 = 7 is incorrect; the correct value is √50 ≈ 7.071.
Mistake 4
Confusing the square root symbol with the cube root
Students often confuse square roots with cube roots.
For example, √50 and ∛50 are different and should not be used interchangeably.
Mistake 5
Making mistakes in long division
The long division method involves several steps, and missing a step can lead to errors. Careful attention to each step is essential.
Square Root of 487 Examples
Problem 1
Can you help Sarah find the area of a square box if its side length is given as √487?
The area of the square is approximately 487 square units.
Explanation
The area of a square is calculated as side^2.
Given the side length is √487, the area is √487 × √487 = 487 square units.
Problem 2
A square-shaped garden measures 487 square feet. If each side is √487, what will be the square feet of half of the garden?
243.5 square feet.
Explanation
To find half the area of the garden, divide the total area by 2: 487 ÷ 2 = 243.5 square feet.
Problem 3
Calculate √487 × 5.
Approximately 110.34.
Explanation
First, find the square root of 487, which is approximately 22.068.
Then, multiply this by 5: 22.068 × 5 ≈ 110.34.
Problem 4
What will be the square root of (484 + 3)?
The square root is approximately 22.07.
Explanation
To find the square root, first calculate the sum: 484 + 3 = 487.
The square root of 487 is approximately 22.07.
Problem 5
Find the perimeter of a rectangle if its length ‘l’ is √487 units and the width ‘w’ is 10 units.
The perimeter of the rectangle is approximately 64.136 units.
Explanation
Perimeter of a rectangle = 2 × (length + width).
Perimeter = 2 × (√487 + 10) ≈ 2 × (22.068 + 10) = 2 × 32.068 ≈ 64.136 units.
FAQ on Square Root of 487
1.What is √487 in its simplest form?
2.Calculate the square of 487.
3.Is 487 a prime number?
4.What are the factors of 487?
5.487 is divisible by?
6.How does learning Algebra help students in Australia make better decisions in daily life?
7.How can cultural or local activities in Australia support learning Algebra topics such as Square Root of 487?
8.How do technology and digital tools in Australia support learning Algebra and Square Root of 487?
9.Does learning Algebra support future career opportunities for students in Australia?
Important Glossaries for the Square Root of 487
- Square root: A square root is the inverse of squaring a number. Example: 4^2 = 16, and the inverse is the square root, √16 = 4.
- Irrational number: A number that cannot be expressed as a simple fraction (p/q, where p and q are integers and q ≠ 0), such as √487.
- Prime number: A number greater than 1 with no divisors other than 1 and itself, such as 487.
- Decimal: A number that includes a fractional part, such as 22.068.
- Long division method: A technique for finding the square root of non-perfect squares by dividing the number into smaller, more manageable parts.
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Jaskaran Singh Saluja
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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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