174 LearnersLast updated on May 26th, 2025
Square Root of 14400
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 14400.
What is the Square Root of 14400?
The square root is the inverse of the square of the number. 14400 is a perfect square. The square root of 14400 is expressed in both radical and exponential forms. In the radical form, it is expressed as √14400, whereas 14400(1/2) in the exponential form. √14400 = 120, which is a rational number because it can be expressed in the form of p/q, where p and q are integers and q ≠ 0.
Finding the Square Root of 14400
The prime factorization method is used for perfect square numbers. Since 14400 is a perfect square, we can use the prime factorization method. Let us learn the following methods:
- Prime factorization method
- Long division method
- Approximation method
Square Root of 14400 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 14400 is broken down into its prime factors.
Step 1: Finding the prime factors of 14400 Breaking it down, we get 2 x 2 x 2 x 2 x 3 x 3 x 5 x 5 x 5 x 5: 24 x 32 x 54
Step 2: Now we found out the prime factors of 14400. The next step is to make pairs of those prime factors. Since 14400 is a perfect square, we can group the digits in pairs. Therefore, √14400 = (22 x 3 x 52) = 120.
Square Root of 14400 by Long Division Method
The long division method is particularly used for 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 14400, we need to group the numbers as 400 and 144.
Step 2: Now we need to find n whose square is less than or equal to 144. We can say n is 12 because 12 x 12 = 144. Now the quotient is 12 after subtracting 144 - 144, the remainder is 0.
Step 3: Now let us bring down 00, which is the new dividend. Add the old divisor with the same number 12 + 12, we get 24, which will be our new divisor.
Step 4: The new divisor will be the sum of the dividend and quotient. Now we get 240 as the new divisor, and we need to find the value of n.
Step 5: The next step is finding 240 x n ≤ 00. Since the dividend is zero, the process stops here. So the square root of √14400 is 120.
Square Root of 14400 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 14400 using the approximation method.
Step 1: Now we have to find the closest perfect square of √14400. The smallest perfect square of 14400 is 14400 itself, so the square root is exactly 120.
Common Mistakes and How to Avoid Them in the Square Root of 14400
Students may 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, √14400 = 120, there is also -120, which should not be forgotten.
Square Root of 14400 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √14400?
The area of the square is 14400 square units.
Explanation
The area of the square = side2.
The side length is given as √14400.
Area of the square = side2 = √14400 x √14400 = 120 x 120 = 14400.
Therefore, the area of the square box is 14400 square units.
Problem 2
A square-shaped building measuring 14400 square feet is built; if each of the sides is √14400, what will be the square feet of half of the building?
7200 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 14400 by 2 = we get 7200.
So half of the building measures 7200 square feet.
Problem 3
Calculate √14400 x 5.
600
Explanation
The first step is to find the square root of 14400, which is 120.
The second step is to multiply 120 with 5. So 120 x 5 = 600.
Problem 4
What will be the square root of (14400 + 0)?
The square root is 120.
Explanation
To find the square root, we need to find the sum of (14400 + 0). 14400 + 0 = 14400, and then √14400 = 120.
Therefore, the square root of (14400 + 0) is ±120.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √14400 units and the width ‘w’ is 50 units.
We find the perimeter of the rectangle as 340 units.
Explanation
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√14400 + 50) = 2 × (120 + 50) = 2 × 170 = 340 units.
FAQ on Square Root of 14400
1.What is √14400 in its simplest form?
2.Mention the factors of 14400.
3.Calculate the square of 14400.
4.Is 14400 a prime number?
5.14400 is divisible by?
6.How does learning Algebra help students in Canada make better decisions in daily life?
7.How can cultural or local activities in Canada support learning Algebra topics such as Square Root of 14400?
8.How do technology and digital tools in Canada support learning Algebra and Square Root of 14400?
9.Does learning Algebra support future career opportunities for students in Canada?
Important Glossaries for the Square Root of 14400
- Square root: A square root is the inverse of a square. Example: 42 = 16 and the inverse of the square is the square root, that is √16 = 4.
- Perfect square: A perfect square is a number that has an integer as its square root, such as 14400, which is 1202
- Rational number: A rational number is a number that can be expressed in the form of p/q, where q is not equal to zero and p and q are integers.
- Long division method: A method used to find the square root of a number by dividing the number into groups starting from the right.
- Prime factorization: The process of expressing a number as a product of its prime factors.
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Jaskaran Singh Saluja
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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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