120 LearnersLast updated on May 26th, 2025
Square Root of 3520
If a number is multiplied by itself, the result is a square. The inverse of squaring a number is finding its square root. Square roots are used in fields like engineering, finance, and physics. Here, we will discuss the square root of 3520.
What is the Square Root of 3520?
The square root is the inverse operation of squaring a number. 3520 is not a perfect square. The square root of 3520 can be expressed in both radical and exponential form. In radical form, it is expressed as √3520, whereas in exponential form it is expressed as (3520)^(1/2). The approximate value of √3520 is 59.3225, which is an irrational number because it cannot be expressed as a simple fraction.
Finding the Square Root of 3520
The prime factorization method is typically used for perfect square numbers. However, for non-perfect square numbers like 3520, other methods such as the long division method and approximation method are used. Let's explore these methods:
- Prime factorization method
- Long division method
- Approximation method
Square Root of 3520 by Prime Factorization Method
The prime factorization of a number involves expressing it as a product of its prime factors. Here's how 3520 is broken down into its prime factors:
Step 1: Finding the prime factors of 3520 Breaking it down, we get 2 x 2 x 2 x 2 x 2 x 5 x 11 = 2^5 x 5^1 x 11^1
Step 2: The prime factors of 3520 are found. Since 3520 is not a perfect square, pairing these factors is not possible to yield a whole number. Hence, applying the prime factorization method to calculate √3520 doesn't yield a simple result.
Square Root of 3520 by Long Division Method
The long division method is particularly useful for non-perfect square numbers. Let's find the square root of 3520 using this method:
Step 1: Begin by grouping the digits of 3520 from right to left, getting 35 and 20.
Step 2: Find a number whose square is close to 35. The closest is 5, since 5 x 5 = 25. Subtract 25 from 35 to get a remainder of 10.
Step 3: Bring down the next pair of digits, 20, to make 1020. Double the divisor (5) to get 10, and find a digit x such that 10x times x is less than or equal to 1020.
Step 4: The new digit x is 9, since 109 x 9 = 981. Subtract 981 from 1020 to get a remainder of 39.
Step 5: Add decimal places and continue the process to find the next digits. The quotient continues as 59.32 after further iterations. Thus, the square root of 3520 is approximately 59.32 using the long division method.
Square Root of 3520 by Approximation Method
The approximation method is a straightforward way to estimate square roots. Let's find the square root of 3520 using this method:
Step 1: Identify the perfect squares nearest to 3520. The smallest perfect square less than 3520 is 3481 (59^2), and the largest perfect square greater than 3520 is 3600 (60^2).
Step 2: Apply the formula: (Given number - smaller perfect square) / (larger perfect square - smaller perfect square). (3520 - 3481) / (3600 - 3481) = 39 / 119 = 0.3277 Add this value to the smaller root: 59 + 0.33 = 59.33 Thus, the square root of 3520 is approximately 59.33 using the approximation method.
Common Mistakes and How to Avoid Them in the Square Root of 3520
Students often make mistakes in calculating square roots, including overlooking the negative square root, skipping steps in the long division method, and more. Let's explore some common mistakes and how to avoid them.
Mistake 1
Forgetting about the negative square root
Always remember that every positive number has both a positive and a negative square root. However, in most practical applications, the positive square root is used.
For instance, √3520 = ±59.32, but we typically use the positive value.
Mistake 2
Not adding the square root symbol correctly
Students sometimes misuse the square root symbol. Always simplify the expression inside the square root first.
For example, √(10 + 26) is not the same as √10 + √26. The correct approach is √(10 + 26) = √36 = 6.
Mistake 3
Incorrectly estimating the value of a non-perfect square
When estimating the square root of a non-perfect square, ensure the number is simplified inside the root first.
For example, √50 ≠ 7; the correct approximation is √50 ≈ 7.071.
Mistake 4
Confusing the square root symbol with the cube root
Always differentiate between square root and cube root symbols.
For example, √3520 and ∛3520 are different operations.
Mistake 5
Mistakes in the long division method
The long division method involves several steps, and missing any can lead to errors. Always follow each step carefully, especially when dealing with remainders and bringing down digits.
Square Root of 3520 Examples
Problem 1
Can you help Alex find the area of a square if its side length is given as √3520?
The area of the square is 3520 square units.
Explanation
The area of a square is calculated as side^2. Given the side length as √3520: Area = (√3520) x (√3520) = 3520 square units.
Problem 2
If a square-shaped field has an area of 3520 square meters, what would be the area of half that field?
1760 square meters
Explanation
To find half the area of the square-shaped field, simply divide the total area by 2: 3520 / 2 = 1760 square meters
Problem 3
Calculate √3520 x 3.
177.9675
Explanation
First, find the square root of 3520, which is approximately 59.3225. Multiply this by 3: 59.3225 x 3 = 177.9675
Problem 4
What will be the square root of (3520 + 80)?
The square root is approximately 60.
Explanation
First, find the sum: 3520 + 80 = 3600. Then find the square root: √3600 = ±60. The positive square root is used in most contexts, so the square root is 60.
Problem 5
Find the perimeter of a rectangle if its length 'l' is √3520 units and the width 'w' is 40 units.
The perimeter of the rectangle is approximately 198.645 units.
Explanation
Perimeter of a rectangle = 2 × (length + width). Length = √3520 ≈ 59.3225, Width = 40.
Perimeter = 2 × (59.3225 + 40) = 2 × 99.3225 = 198.645 units.
FAQ on Square Root of 3520
1.What is √3520 in its simplest form?
2.Mention the factors of 3520.
3.Calculate the square of 3520.
4.Is 3520 a prime number?
5.By which numbers is 3520 divisible?
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 3520?
8.How do technology and digital tools in Australia support learning Algebra and Square Root of 3520?
9.Does learning Algebra support future career opportunities for students in Australia?
Important Glossaries for the Square Root of 3520
- Square root: A square root is the operation that finds a number which, when multiplied by itself, gives the original number. For example, the square root of 16 is 4, because 4 x 4 = 16.
- Irrational number: An irrational number cannot be expressed as a simple fraction, meaning it cannot be written as a ratio of two integers.
- Radical: A symbol (√) used to denote the square root or nth root of a number.
- Perfect square: A number that is the square of an integer. For example, 16 is a perfect square because it is 4 squared (4 x 4).
- Long division method: A technique used to find the square root of a number by dividing and averaging, often used for non-perfect squares.
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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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