120 LearnersLast updated on May 26th, 2025
Square Root of 3145
If a number is multiplied by itself, the result is a square. The inverse of the square is a square root. Square roots are used in various fields such as engineering, finance, etc. Here, we will discuss the square root of 3145.
What is the Square Root of 3145?
The square root is the inverse of squaring a number. 3145 is not a perfect square. The square root of 3145 is expressed in both radical and exponential form. In the radical form, it is expressed as √3145, whereas in exponential form as (3145)^(1/2). √3145 ≈ 56.072, which is an irrational number because it cannot be expressed as a fraction of two integers.
Finding the Square Root of 3145
For perfect square numbers, the prime factorization method is commonly used. However, for non-perfect square numbers like 3145, methods such as the long division method and approximation method are utilized. Let us now explore these methods:
- Prime factorization method
- Long division method
- Approximation method
Square Root of 3145 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Let's break down 3145 into its prime factors:
Step 1: Finding the prime factors of 3145 Breaking it down, we get 5 x 13 x 29 x 1: 5^1 x 13^1 x 29^1
Step 2: Since 3145 is not a perfect square, the digits of the number cannot be grouped into pairs. Therefore, calculating 3145 using prime factorization is impractical.
Square Root of 3145 by Long Division Method
The long division method is particularly useful for non-perfect square numbers. Here is how to find the square root using the long division method, step by step:
Step 1: Group the digits of 3145 starting from the right. So, we have 31 and 45.
Step 2: Find the largest number whose square is less than or equal to 31. This number is 5, as 5^2 = 25.
Step 3: Subtract 25 from 31, leaving a remainder of 6. Bring down the next pair, 45, to make the new dividend 645.
Step 4: Double the previous quotient (5) to get 10, which becomes part of the new divisor.
Step 5: Find a digit (n) such that 10n * n gives a product less than or equal to 645. The value of n is 6.
Step 6: Subtract the product, 636, from 645, leaving a remainder of 9. Bring down two zeros to continue.
Step 7: Continue this process to calculate a precise decimal value. The quotient grows to reflect the square root. Thus, the square root of 3145 is approximately 56.072.
Square Root of 3145 by Approximation Method
The approximation method is another way to find square roots. Here's how to find the square root of 3145 using this method:
Step 1: Identify the closest perfect squares around 3145. The nearest perfect squares are 3136 (56^2) and 3249 (57^2). So, √3145 falls between 56 and 57.
Step 2: Use the formula: (Given number - smaller perfect square) / (Larger perfect square - smaller perfect square). Applying the formula: (3145 - 3136) / (3249 - 3136) ≈ 0.081 Adding this decimal to the lower square root gives 56 + 0.081 = 56.081. However, upon more precise calculation, the square root of 3145 is approximately 56.072.
Common Mistakes and How to Avoid Them in the Square Root of 3145
Students often make mistakes when finding square roots, such as forgetting about the negative square root or misapplying methods. Let's address a few common errors:
Mistake 1
Forgetting about the negative square root
Students should remember that every positive number has both a positive and negative square root. However, in many applications, only the positive square root is used.
For instance, √50 = ±7.071.
Mistake 2
Not adding the square root symbol in proper places
Correct usage of the square root symbol is crucial. Teach students to simplify numbers inside the square root before proceeding.
For example: √(12 + 24) should not be split into √12 + √24, which is incorrect. The correct approach is √(12 + 24) = √36 = 6.
Mistake 3
Not finding the correct value of a non-perfect square
Begin by simplifying the numbers under the square root to avoid errors in approximation.
For example: √50 ≈ 7.071.
Mistake 4
Confusing the square root symbol with the cube root
It's crucial to differentiate between cube roots and square roots.
For example: √50 and ∛50 are different concepts.
Mistake 5
Making mistakes in long division
The long division method involves detailed steps, and skipping any can lead to errors. Ensure students understand each step and practice thoroughly.
Square Root of 3145 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √3145?
The area of the square is approximately 3145 square units.
Explanation
The area of a square is calculated as side^2.
Given the side length as √3145, the area is:
Area = (√3145) * (√3145) = 3145 square units.
Problem 2
A square-shaped building measuring 3145 square feet is built; if each side is √3145, what will be the square feet of half of the building?
1572.5 square feet
Explanation
Divide the total area by 2 to find half of the building's area: 3145 / 2 = 1572.5 square feet.
Problem 3
Calculate √3145 × 10.
Approximately 560.72
Explanation
First, find the square root of 3145, which is approximately 56.072, then multiply by 10: 56.072 × 10 = 560.72.
Problem 4
What will be the square root of (3140 + 5)?
The square root is approximately 56.072
Explanation
To find the square root, sum 3140 and 5 to get 3145, then calculate the square root: √3145 ≈ 56.072.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √3145 units and the width ‘w’ is 50 units.
The perimeter of the rectangle is approximately 212.144 units.
Explanation
Perimeter of the rectangle = 2 × (length + width) Perimeter = 2 × (√3145 + 50) ≈ 2 × (56.072 + 50) = 2 × 106.072 = 212.144 units.
FAQ on Square Root of 3145
1.What is √3145 in its simplest form?
2.Mention the factors of 3145.
3.Calculate the square of 3145.
4.Is 3145 a prime number?
5.3145 is divisible by?
6.How does learning Algebra help students in Vietnam make better decisions in daily life?
7.How can cultural or local activities in Vietnam support learning Algebra topics such as Square Root of 3145?
8.How do technology and digital tools in Vietnam support learning Algebra and Square Root of 3145?
9.Does learning Algebra support future career opportunities for students in Vietnam?
Important Glossaries for the Square Root of 3145
- Square root: The square root of a number is a value that, when multiplied by itself, gives the original number. For example, √9 = 3.
- Irrational number: An irrational number cannot be expressed as a simple fraction; its decimal form is non-repeating and non-terminating. For example, √2.
- Prime factorization: Expressing a number as the product of its prime factors. Example: The prime factorization of 3145 is 5 x 13 x 29.
- Long division method: A step-by-step approach to finding the square root of a number by dividing, multiplying, and subtracting iteratively.
- Perfect square: A number that is the square of an integer. Example: 49 is a perfect square because it is 7^2.
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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.
Fun Fact
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