104 LearnersLast updated on May 26th, 2025
Square Root of 5200
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 vehicle design, finance, etc. Here, we will discuss the square root of 5200.
What is the Square Root of 5200?
The square root is the inverse of the square of the number. 5200 is not a perfect square. The square root of 5200 is expressed in both radical and exponential form. In the radical form, it is expressed as √5200, whereas (5200)^(1/2) is the exponential form. √5200 ≈ 72.11103, 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 5200
The prime factorization method is used for perfect square numbers. However, the prime factorization method is not used for non-perfect square numbers where 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 5200 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 5200 is broken down into its prime factors:
Step 1: Finding the prime factors of 5200
Breaking it down, we get 2 x 2 x 2 x 2 x 5 x 5 x 13: 2^4 x 5^2 x 13
Step 2: Now that we have found the prime factors of 5200, the second step is to make pairs of those prime factors. Since 5200 is not a perfect square, therefore the digits of the number can’t be grouped in pairs entirely. However, we can pair two 2's and two 5's to simplify it partially.
Square Root of 5200 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 5200, we need to group it as 52 and 00.
Step 2: Now we need to find n whose square is 52. We can say n is '7' because 7 x 7 = 49, which is less than 52. Now the quotient is 7, after subtracting 52 - 49, the remainder is 3.
Step 3: Now let us bring down the next pair of zeros, making it 300, which is the new dividend. Add the old divisor with the same number 7 + 7 = 14, which will be our new divisor.
Step 4: The new divisor will be 14n, and we need to find the value of n.
Step 5: The next step is finding 14n x n ≤ 300. Let’s consider n as 2, now 142 x 2 = 284.
Step 6: Subtract 300 from 284, the difference is 16, and the quotient is 72.
Step 7: Since the dividend is less than the divisor, we need to add a decimal point. Adding the decimal point allows us to add two zeroes to the dividend. Now the new dividend is 1600.
Step 8: The next divisor is 144 because 1444 x 4 = 5776 is too large. Let’s try 72.1 x 72.1, and continue with the process.
Step 9: Subtracting 5776 from 1600, we continue with the long division until we reach the desired precision.
So the square root of √5200 ≈ 72.111.
Square Root of 5200 by Approximation Method
The approximation method is another method for finding square roots. It is an easy method to find the square root of a given number. Now let us learn how to find the square root of 5200 using the approximation method.
Step 1: Now we have to find the closest perfect square of √5200. The smallest perfect square less than 5200 is 4900 and the largest perfect square greater than 5200 is 5290. √5200 falls somewhere between 70 and 73.
Step 2: Now we need to apply the formula that is (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Using the formula (5200 - 4900) / (5290 - 4900) = 0.75. Using the formula, we identified the decimal point of our square root. The next step is adding the value we got initially to the decimal number which is 70 + 0.75 ≈ 70.75, so the square root of 5200 is approximately 72.11.
Common Mistakes and How to Avoid Them in the Square Root of 5200
Students do make mistakes while finding the square root, such as forgetting about the negative square root or skipping long division methods. Now let us look at a few of those mistakes that students tend to make in detail.
Mistake 1
Forgetting about the negative square root
It is important to make students aware that a number does have both positive and negative square roots. However, we will be taking only the positive square root, as it is the required one.
For example: √50 = 7.07, but there is also -7.07 which should not be forgotten.
Square Root of 5200 Examples
Problem 1
Can you help Lisa find the area of a square box if its side length is given as √5200?
The area of the square is 5200 square units.
Explanation
The area of the square = side^2.
The side length is given as √5200.
Area of the square = side^2 = √5200 x √5200 = 5200.
Therefore, the area of the square box is 5200 square units.
Problem 2
A square-shaped building measuring 5200 square feet is built; if each of the sides is √5200, what will be the square feet of half of the building?
2600 square feet.
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 5200 by 2 = we get 2600.
So half of the building measures 2600 square feet.
Problem 3
Calculate √5200 x 5.
360.555.
Explanation
The first step is to find the square root of 5200 which is approximately 72.111.
The second step is to multiply 72.111 with 5.
So 72.111 x 5 ≈ 360.555.
Problem 4
What will be the square root of (5000 + 200)?
The square root is approximately 72.111.
Explanation
To find the square root, we need to find the sum of (5000 + 200) = 5200, and then √5200 ≈ 72.111.
Therefore, the square root of (5000 + 200) is approximately ±72.111.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √5200 units and the width ‘w’ is 100 units.
The perimeter of the rectangle is approximately 344.222 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√5200 + 100) ≈ 2 × (72.111 + 100) ≈ 2 × 172.111 ≈ 344.222 units.
FAQ on Square Root of 5200
1.What is √5200 in its simplest form?
2.Mention the factors of 5200.
3.Calculate the square of 5200.
4.Is 5200 a prime number?
5.5200 is divisible by?
6.How does learning Algebra help students in United Kingdom make better decisions in daily life?
7.How can cultural or local activities in United Kingdom support learning Algebra topics such as Square Root of 5200?
8.How do technology and digital tools in United Kingdom support learning Algebra and Square Root of 5200?
9.Does learning Algebra support future career opportunities for students in United Kingdom?
Important Glossaries for the Square Root of 5200
- Square root: A square root is the inverse of a square. Example: 4^2 = 16, and the inverse of the square is the square root, that is √16 = 4.
- 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; however, it is always the positive square root that has more prominence due to its uses in the real world. That is the reason it is also known as the principal square root.
- Prime factorization: Prime factorization is the process of expressing a number as the product of its prime factors.
- Approximation: Approximation is finding a value that is close enough to the right answer, usually with some thought or calculation involved.
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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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