144 LearnersLast updated on May 26th, 2025
Square Root of 19600
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 19600.
What is the Square Root of 19600?
The square root is the inverse of the square of the number. 19600 is a perfect square. The square root of 19600 is expressed in both radical and exponential form. In the radical form, it is expressed as √19600, whereas (19600)(1/2) in the exponential form. √19600 = 140, 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 19600
The prime factorization method can be used for perfect square numbers. However, methods like the long division method and approximation are used for non-perfect square numbers. Let us now learn the following methods: -
- Prime factorization method
- Long division method
- Approximation method
Square Root of 19600 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 19600 is broken down into its prime factors.
Step 1: Finding the prime factors of 19600 Breaking it down, we get 2 x 2 x 2 x 2 x 5 x 5 x 7 x 7: 24 x 52 x 72
Step 2: Now we have found the prime factors of 19600. The second step is to make pairs of those prime factors. Since 19600 is a perfect square, the digits of the number can be grouped in pairs.
Therefore, calculating 19600 using prime factorization gives us √19600 = 22 x 5 x 7 = 140.
Square Root of 19600 by Long Division Method
The long division method is particularly used for finding square roots. 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 19600, we need to group it as 00 and 196.
Step 2: Now we need to find n whose square is closest to 196. We can say n is '14' because 14 x 14 = 196.
Step 3: The quotient is 14, and since there is no remainder, the square root of 19600 is exactly 140.
Square Root of 19600 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. However, since 19600 is a perfect square, the exact square root is 140.
Common Mistakes and How to Avoid Them in the Square Root of 19600
Students can make mistakes while finding the square root, such as forgetting about the negative square root or skipping steps in methods. Now let us look at a few of those mistakes that students tend to make in detail.
Square Root of 19600 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √19600?
The area of the square is 19600 square units.
Explanation
The area of the square = side².
The side length is given as √19600.
Area of the square = side² = 140 x 140 = 19600.
Therefore, the area of the square box is 19600 square units.
Problem 2
A square-shaped building measuring 19600 square feet is built; if each of the sides is √19600, what will be the square feet of half of the building?
9800 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 19600 by 2 = we get 9800.
So half of the building measures 9800 square feet.
Problem 3
Calculate √19600 x 5.
700
Explanation
The first step is to find the square root of 19600, which is 140.
The second step is to multiply 140 with 5. So 140 x 5 = 700.
Problem 4
What will be the square root of (19600 + 400)?
The square root is 142.
Explanation
To find the square root, we need to find the sum of (19600 + 400).
19600 + 400 = 20000, and then √20000 ≈ 141.42.
Therefore, the square root of (19600 + 400) is approximately ±141.42.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √19600 units and the width ‘w’ is 38 units.
The perimeter of the rectangle is 356 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√19600 + 38) = 2 × (140 + 38) = 2 × 178 = 356 units.
FAQ on Square Root of 19600
1.What is √19600 in its simplest form?
2.Mention the factors of 19600.
3.Calculate the square of 140.
4.Is 19600 a prime number?
5.19600 is divisible by?
Important Glossaries for the Square Root of 19600
- Square root: A square root is the inverse of a square. Example: 122 = 144, and the inverse of the square is the square root, that is, √144 = 12.
- Rational number: A rational number is a number that can 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. This is why it is also known as the principal square root.
- Perfect square: A perfect square is a number that is the square of an integer. Example: 19600 is a perfect square because it is 1402.
- Long division method: A systematic method used to find the square root of a number by dividing it into groups and solving step by step.
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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.
Fun Fact
: He loves to play the quiz with kids through algebra to make kids love it.
