128 LearnersLast updated on May 26th, 2025
Square Root of 13000
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 various fields such as vehicle design, finance, etc. Here, we will discuss the square root of 13000.
What is the Square Root of 13000?
The square root is the inverse of the square of the number. 13000 is not a perfect square. The square root of 13000 is expressed in both radical and exponential form. In the radical form, it is expressed as √13000, whereas (13000)(1/2) in the exponential form. √13000 ≈ 114.0175, 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 13000
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 13000 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 13000 is broken down into its prime factors:
Step 1: Finding the prime factors of 13000 Breaking it down, we get 2 x 2 x 2 x 5 x 5 x 5 x 13: 23 x 53 x 13
Step 2: Now that we have found the prime factors of 13000, the second step is to make pairs of those prime factors. Since 13000 is not a perfect square, the digits of the number can’t be grouped in pairs.
Therefore, calculating 13000 using prime factorization is not straightforward.
Square Root of 13000 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 13000, we need to group it as 00 and 130.
Step 2: Now we need to find n whose square is less than or equal to 130. We choose n as 11 because 11 x 11 = 121 which is less than 130. Now the quotient is 11, and after subtracting 121 from 130, the remainder is 9.
Step 3: Bring down the next pair, 00, making the new dividend 900.
Step 4: Double the quotient from step 2, which is 11, giving us 22. We now need to find a digit x such that 22x times x is less than or equal to 900.
Step 5: Choose x as 4, because 224 x 4 = 896 is less than 900. Subtracting 896 from 900, the difference is 4.
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 400.
Step 7: Continue finding new divisors and digits until the desired decimal accuracy is achieved.
The square root of 13000 is approximately 114.017.
Square Root of 13000 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 13000 using the approximation method.
Step 1: Now we have to find the closest perfect square of √13000. The smallest perfect square less than 13000 is 12100 (1102) and the largest perfect square greater than 13000 is 14400 (1202). √13000 falls somewhere between 110 and 120.
Step 2: Now we need to apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Going by the formula (13000 - 12100) / (14400 - 12100) = 0.3913.
Using the formula, we identified the decimal part of our square root.
The next step is adding the value we got initially to the decimal number which is 110 + 0.3913 = 114.017, so the square root of 13000 is approximately 114.017.
Common Mistakes and How to Avoid Them in the Square Root of 13000
Students make mistakes while finding the square root, such as forgetting about the negative square root or skipping steps in the long division method. 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: √13000 = 114.017, there is also -114.017 which should not be forgotten.
Square root of 13000 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √13000?
The area of the square is 13000 square units.
Explanation
The area of the square = side2.
The side length is given as √13000.
Area of the square = side2 = √13000 x √13000 = 13000.
Therefore, the area of the square box is 13000 square units.
Problem 2
A square-shaped building measuring 13000 square feet is built; if each of the sides is √13000, what will be the square feet of half of the building?
6500 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 13000 by 2, we get 6500.
So half of the building measures 6500 square feet.
Problem 3
Calculate √13000 x 5.
570.0875
Explanation
The first step is to find the square root of 13000 which is approximately 114.017, the second step is to multiply 114.017 with 5.
So 114.017 x 5 = 570.0875.
Problem 4
What will be the square root of (13000 + 100)?
The square root is approximately 114.453.
Explanation
To find the square root, we need to find the sum of (13000 + 100).
13000 + 100 = 13100, and then √13100 ≈ 114.453.
Therefore, the square root of (13000 + 100) is approximately ±114.453.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √13000 units and the width ‘w’ is 50 units.
The perimeter of the rectangle is approximately 328.035 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√13000 + 50) = 2 × (114.017 + 50) = 2 × 164.017 = 328.035 units.
FAQ on Square Root of 13000
1.What is √13000 in its simplest form?
2.Mention the factors of 13000.
3.Calculate the square of 130.
4.Is 13000 a prime number?
5.13000 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 13000?
8.How do technology and digital tools in Vietnam support learning Algebra and Square Root of 13000?
9.Does learning Algebra support future career opportunities for students in Vietnam?
Important Glossaries for the Square Root of 13000
- 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. Example: 4, 9, 16.
- Approximation method: An easy method to find an approximate value of a square root when the exact value is not needed or difficult to determine.
- Long division method: A step-by-step method used to find the square root of non-perfect squares, involving grouping and dividing numbers in a specific manner.
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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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