126 LearnersLast updated on May 26th, 2025
Square Root of 520
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 the field of vehicle design, finance, etc. Here, we will discuss the square root of 520.
What is the Square Root of 520?
The square root is the inverse of the square of the number. 520 is not a perfect square. The square root of 520 is expressed in both radical and exponential form. In the radical form, it is expressed as √520, whereas in the exponential form it is expressed as (520)(1/2). √520 ≈ 22.8035, 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 520
The prime factorization method is used for perfect square numbers. However, for non-perfect square numbers, the prime factorization method is not used; instead, methods like the long division method and approximation method are employed. Let us now learn these methods:
- Prime factorization method
- Long division method
- Approximation method
Square Root of 520 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 520 is broken down into its prime factors.
Step 1: Finding the prime factors of 520 Breaking it down, we get 2 x 2 x 2 x 5 x 13: 2^3 x 5 x 13
Step 2: Now we found out the prime factors of 520. The second step is to make pairs of those prime factors. Since 520 is not a perfect square, the digits of the number can’t be grouped in pairs.
Therefore, calculating 520 using prime factorization is not straightforward.
Square Root of 520 by Long Division Method
The long division method is particularly used for non-perfect square numbers. In this method, we should check the closest perfect square number for the given number. Let us now learn how to find the square root using the long division method, step by step.
Step 1: To begin with, we need to group the numbers from right to left. In the case of 520, we group it as 20 and 5.
Step 2: Now, we need to find n whose square is ≤ 5. We can say n as '2' because 2 x 2 = 4, which is less than or equal to 5. Now the quotient is 2, and subtracting 4 from 5 gives us a remainder of 1.
Step 3: Bring down 20, making the new dividend 120. Add the old divisor with the same number: 2 + 2 = 4, which will be our new divisor.
Step 4: The new divisor will be 4n. We need to find n such that 4n x n ≤ 120. Let us consider n as 2, now 42 x 2 = 84.
Step 5: Subtract 84 from 120, the difference is 36. The quotient is 22.
Step 6: Since the dividend is less than the divisor, we need to add a decimal point. Adding the decimal point allows us to add two zeros to the dividend. Now the new dividend is 3600.
Step 7: We need to find the new divisor. Let it be 446 because 446 x 6 = 2676.
Step 8: Subtracting 2676 from 3600 gives us a remainder of 924.
Step 9: The quotient is now 22.8.
Step 10: Continue with these steps until the desired decimal places are reached.
So the square root of √520 is approximately 22.80.
Square Root of 520 by Approximation Method
The approximation method is an easy method for finding the square roots of numbers. Let us learn how to find the square root of 520 using the approximation method.
Step 1: Find the closest perfect square numbers to √520. The smallest perfect square less than 520 is 484 (222) and the largest perfect square greater than 520 is 529 (232). √520 falls somewhere between 22 and 23.
Step 2: Apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square).
Using the formula (520 - 484) / (529 - 484) = 36 / 45 = 0.8. Adding this to 22 gives 22 + 0.8 = 22.8,
so the square root of 520 is approximately 22.8.
Common Mistakes and How to Avoid Them in Finding the Square Root of 520
Students often make mistakes while finding the square root, such as forgetting about the negative square root or skipping steps in the long division method. Let us look at a few of those mistakes in detail.
Mistake 1
Forgetting about the negative square root
It is important to remember that a number has both positive and negative square roots. However, we usually consider only the positive square root, as it is typically required in practical applications.
For example: √25 = 5, but there is also -5 which should not be forgotten.
Square Root of 520 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √520?
The area of the square is approximately 520 square units.
Explanation
The area of a square = side2.
The side length is given as √520.
Area of the square = side2 = √520 x √520 = 520.
Therefore, the area of the square box is approximately 520 square units.
Problem 2
A square-shaped building measuring 520 square feet is built; if each of the sides is √520, what will be the square feet of half of the building?
260 square feet
Explanation
We can simply divide the given area by 2 as the building is square-shaped.
Dividing 520 by 2 gives us 260.
So half of the building measures 260 square feet.
Problem 3
Calculate √520 x 5.
114.015
Explanation
First, find the square root of 520, which is approximately 22.8035.
Multiply 22.8035 by 5.
So 22.8035 x 5 ≈ 114.015.
Problem 4
What will be the square root of (500 + 20)?
The square root is approximately 22.8035
Explanation
To find the square root,
calculate the sum: (500 + 20) = 520.
The square root of 520 is approximately ±22.8035.
Problem 5
Find the perimeter of a rectangle if its length ‘l’ is √520 units and the width ‘w’ is 30 units.
The perimeter of the rectangle is approximately 105.607 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√520 + 30) ≈ 2 × (22.8035 + 30) ≈ 2 × 52.8035 ≈ 105.607 units.
FAQ on Square Root of 520
1.What is √520 in its simplest form?
2.Mention the factors of 520.
3.Calculate the square of 520.
4.Is 520 a prime number?
5.520 is divisible by?
6.How does learning Algebra help students in Oman make better decisions in daily life?
7.How can cultural or local activities in Oman support learning Algebra topics such as Square Root of 520?
8.How do technology and digital tools in Oman support learning Algebra and Square Root of 520?
9.Does learning Algebra support future career opportunities for students in Oman?
Important Glossaries for the Square Root of 520
- Square root: A square root is the inverse of a square. For example, 52 = 25, and the inverse of the square is the square root, which is √25 = 5.
- Irrational number: An irrational number is a number that cannot be written in the form of p/q, where q is not equal to zero, and p and q are integers
- .Principal square root: A number has both positive and negative square roots, but the positive square root is often more prominent due to its practical applications, making it the principal square root.
- Prime factorization: Breaking down a number into its prime factors, which are numbers that have only two divisors: 1 and themselves.
- Decimal: A decimal is a number that consists of a whole number and a fraction written together, for example, 7.86, 8.65, and 9.42 are decimals.
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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
: He loves to play the quiz with kids through algebra to make kids love it.
