104 LearnersLast updated on May 26th, 2025
Square Root of 5128
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 5128.
What is the Square Root of 5128?
The square root is the inverse of the square of the number. 5128 is not a perfect square. The square root of 5128 is expressed in both radical and exponential form. In the radical form, it is expressed as √5128, whereas (5128)^(1/2) in the exponential form. √5128 ≈ 71.6197, 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 5128
The prime factorization method is used for perfect square numbers. However, the prime factorization method is not used for non-perfect square numbers where 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 5128 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 5128 is broken down into its prime factors:
Step 1: Finding the prime factors of 5128
Breaking it down, we get 2 x 2 x 2 x 641: 2^3 x 641
Step 2: Now we found the prime factors of 5128. The second step is to make pairs of those prime factors. Since 5128 is not a perfect square, therefore the digits of the number can’t be grouped in pairs. Therefore, calculating 5128 using prime factorization is not straightforward.
Square Root of 5128 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 5128, we need to group it as 28 and 51.
Step 2: Now we need to find n whose square is less than or equal to 51. We can say n as ‘7’ because 7 x 7 = 49, which is less than 51. Now the quotient is 7, and the remainder is 2 after subtracting 49 from 51.
Step 3: Now let us bring down 28, making the new dividend 228. Add the old divisor with the same number 7 + 7, we get 14 which will be our new divisor.
Step 4: We now have 14x as the new divisor. We need to find x such that 14x x x is less than or equal to 228. Let x be 1, then 141 x 1 = 141.
Step 5: Subtract 141 from 228, the difference is 87, and the quotient is 71.
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 zeroes to the dividend. Now the new dividend is 8700.
Step 7: We continue the division to reach more decimal places if needed.
So the square root of √5128 is approximately 71.6197.
Square Root of 5128 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 5128 using the approximation method.
Step 1: Now we have to find the closest perfect squares of √5128. The smallest perfect square less than 5128 is 4900 (70^2), and the largest perfect square greater than 5128 is 5184 (72^2). √5128 falls somewhere between 70 and 72.
Step 2: Now we need to apply the formula that is (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Going by the formula (5128 - 4900) / (5184 - 4900) = 228 / 284 ≈ 0.8028. 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 + 0.8028 ≈ 71.8028, so the square root of 5128 is approximately 71.8028.
Common Mistakes and How to Avoid Them in the Square Root of 5128
Students do make mistakes while finding the square root, such as forgetting about the negative square root, skipping long division methods, etc. 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 ≈ 7.071, there is also -7.071, which should not be forgotten.
Square Root of 5128 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √5128?
The area of the square is approximately 5128 square units.
Explanation
The area of the square = side^2.
The side length is given as √5128.
Area of the square = side^2 = √5128 x √5128 = 5128.
Therefore, the area of the square box is approximately 5128 square units.
Problem 2
A square-shaped building measuring 5128 square feet is built; if each of the sides is √5128, what will be the square feet of half of the building?
2564 square feet.
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 5128 by 2 = 2564.
So half of the building measures 2564 square feet.
Problem 3
Calculate √5128 x 5.
Approximately 358.0985.
Explanation
The first step is to find the square root of 5128, which is approximately 71.6197.
The second step is to multiply 71.6197 with 5.
So 71.6197 x 5 ≈ 358.0985.
Problem 4
What will be the square root of (5120 + 8)?
Approximately 71.6197.
Explanation
To find the square root, we need to find the sum of (5120 + 8). 5120 + 8 = 5128, and then √5128 ≈ 71.6197.
Therefore, the square root of (5120 + 8) is approximately ±71.6197.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √5128 units and the width ‘w’ is 38 units.
We find the perimeter of the rectangle as approximately 219.2394 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√5128 + 38) ≈ 2 × (71.6197 + 38) = 2 × 109.6197 ≈ 219.2394 units.
FAQ on Square Root of 5128
1.What is √5128 in its simplest form?
2.Mention the factors of 5128.
3.Calculate the square of 5128.
4.Is 5128 a prime number?
5.5128 is divisible by?
6.How does learning Algebra help students in India make better decisions in daily life?
7.How can cultural or local activities in India support learning Algebra topics such as Square Root of 5128?
8.How do technology and digital tools in India support learning Algebra and Square Root of 5128?
9.Does learning Algebra support future career opportunities for students in India?
Important Glossaries for the Square Root of 5128
- 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.
- Perfect square: A perfect square is a number that is the square of an integer. For example, 4, 9, 16 are perfect squares.
- Long division method: A method used to find the square root of non-perfect squares by dividing the number into smaller, manageable parts and solving step-by-step.
- Approximation method: A method to estimate the square root of a non-perfect square by identifying nearby perfect squares and interpolating between them.
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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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