132 LearnersLast updated on May 26th, 2025
Square Root of 14600
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 14600.
What is the Square Root of 14600?
The square root is the inverse of the square of the number. 14600 is not a perfect square. The square root of 14600 is expressed in both radical and exponential form. In the radical form, it is expressed as √14600, whereas (14600)(1/2) in the exponential form. √14600 ≈ 120.83, 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 14600
The prime factorization method is used for perfect square numbers. However, the prime factorization method is not typically used for non-perfect square numbers where long-division and approximation methods are utilized. Let us now learn the following methods:
- Prime factorization method
- Long division method
- Approximation method
Square Root of 14600 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 14600 is broken down into its prime factors.
Step 1: Finding the prime factors of 14600 Breaking it down, we get 2 x 2 x 2 x 5 x 5 x 73: 23 x 52 x 73
Step 2: Now we found the prime factors of 14600. The second step is to make pairs of those prime factors. Since 14600 is not a perfect square, calculating its square root using prime factorization directly is not feasible.
Square Root of 14600 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 14600, we need to group it as 00, 46, and 1.
Step 2: Now we need to find n whose square is less than or equal to 1. We can say n as ‘1’ because 1 x 1 is equal to 1. Now the quotient is 1, and after subtracting 1 - 1, the remainder is 0.
Step 3: Now let us bring down 46, which is the new dividend. Add the old divisor with the same number 1 + 1 to get 2, which will be our new divisor.
Step 4: The new divisor will be the sum of the dividend and quotient. Now we get 2n as the new divisor, and we need to find the value of n.
Step 5: The next step is finding 2n x n ≤ 46. Let us consider n as 2, now 2 x 2 x 2 = 44.
Step 6: Subtract 46 from 44; the difference is 2.
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 200.
Step 8: Now we need to find the new divisor. Continuing with this process will eventually lead to an approximate value of the square root, which is 120.83.
Square Root of 14600 by Approximation Method
The approximation method is another way of 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 14600 using the approximation method.
Step 1: Now we have to find the closest perfect squares around √14600. The smallest perfect square less than 14600 is 14400 (1202), and the largest perfect square greater than 14600 is 14884 (1222). √14600 falls somewhere between 120 and 122.
Step 2: Now we need to apply the formula: (Given number - smallest perfect square) ÷ (Greater perfect square - smallest perfect square)
Using the formula (14600 - 14400) ÷ (14884 - 14400) = 0.83
Adding the decimal to the initial integer estimate gives us 120 + 0.83 = 120.83, so the square root of 14600 is approximately 120.83.
Common Mistakes and How to Avoid Them in the Square Root of 14600
Students often make mistakes while finding the square root, such as forgetting about the negative square root, skipping steps in the long division method, 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 has both positive and negative square roots. However, we usually take 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 14600 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √14500?
The area of the square is 14400.25 square units.
Explanation
The area of the square = side2.
The side length is given as √14500.
Area of the square = side2 = √14500 × √14500 ≈ 120.415 × 120.415 = 14500.25
Therefore, the area of the square box is 14500.25 square units.
Problem 2
A square-shaped building measuring 14600 square feet is built; if each of the sides is √14600, what will be the square feet of half of the building?
7300 square feet
Explanation
We can divide the given area by 2 as the building is square-shaped.
Dividing 14600 by 2 gives us 7300.
So, half of the building measures 7300 square feet.
Problem 3
Calculate √14600 × 5.
604.15
Explanation
The first step is to find the square root of 14600, which is approximately 120.83.
The second step is to multiply 120.83 by 5.
So, 120.83 × 5 = 604.15.
Problem 4
What will be the square root of (14500 + 100)?
The square root is 121.24
Explanation
To find the square root, we need to find the sum of (14500 + 100).
14500 + 100 = 14600, and then √14600 ≈ 121.24.
Therefore, the square root of (14500 + 100) is approximately ±121.24.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √14500 units and the width ‘w’ is 100 units.
The perimeter of the rectangle is 441.66 units.
Explanation
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√14500 + 100) = 2 × (120.415 + 100) = 2 × 220.415 = 440.83 units.
FAQ on Square Root of 14600
1.What is √14600 in its simplest form?
2.Mention the factors of 14600.
3.Calculate the square of 14600.
4.Is 14600 a prime number?
5.14600 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 14600?
8.How do technology and digital tools in Vietnam support learning Algebra and Square Root of 14600?
9.Does learning Algebra support future career opportunities for students in Vietnam?
Important Glossaries for the Square Root of 14600
- Square root: A square root is the inverse operation of squaring a number. For example, 42 = 16, and the inverse square root of 16 is √16 = 4.
- Irrational number: An irrational number cannot be expressed as a simple fraction or ratio of two integers. Its decimal form is non-terminating and non-repeating, such as √14600.
- Perfect square: A perfect square is the product of an integer multiplied by itself. For example, 144 is a perfect square of 12.
- Approximation: This refers to finding an estimated value or result that is close to the actual one, often used when dealing with irrational numbers.
- Long division: A method used to find the square root of numbers that are not perfect squares, involving division and subtraction processes.
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About BrightChamps in Vietnam
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.
