147 LearnersLast updated on May 26th, 2025
Square Root of 16900
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 16900.
What is the Square Root of 16900?
The square root is the inverse of the square of the number. 16900 is a perfect square. The square root of 16900 is expressed in both radical and exponential form. In the radical form, it is expressed as √16900, whereas (16900)(1/2) in the exponential form. √16900 = 130, 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 16900
The prime factorization method is used for perfect square numbers. The long division method and approximation method can also be used for both perfect and non-perfect squares. Let's explore these methods:
- Prime factorization method
- Long division method
- Approximation method
Square Root of 16900 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let's see how 16900 is broken down into its prime factors.
Step 1: Finding the prime factors of 16900 Breaking it down, we get 2 x 2 x 5 x 5 x 13 x 13: 22 x 52 x 132
Step 2: Now that we have found the prime factors of 16900, the next step is to make pairs of those prime factors. Since 16900 is a perfect square, the digits of the number can be grouped into pairs.
Therefore, calculating √16900 using prime factorization is possible, resulting in 130.
Square Root of 16900 by Long Division Method
The long division method is used for both perfect and non-perfect square numbers. Let's 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 16900, we need to group it as 169 and 00.
Step 2: Now we need to find n whose square is 169. We can say n is ‘13’ because 13 x 13 = 169. The quotient is 13, and after subtracting 169 from 169, the remainder is 0.
Step 3: Since the remainder is zero, no further steps are needed. The square root of 16900 is 130.
Square Root of 16900 by Approximation Method
The approximation method is another way to find square roots; it is an easy method to find the square root of a given number. However, since 16900 is a perfect square, we can directly use its exact value, which is 130.
Common Mistakes and How to Avoid Them in the Square Root of 16900
Students do make mistakes while finding the square root, such as forgetting about the negative square root or skipping steps. Let's look at a few of these mistakes 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 typically use only the positive square root, as it is the required one. For example: √16900 = 130, there is also -130 which should not be forgotten.
Square Root of 16900 Examples
Problem 1
Can you help Max find the side length of a square box if its area is given as 16900 square units?
The side length of the square box is 130 units.
Explanation
The side length of the square = √area = √16900 = 130.
Therefore, the side length of the square box is 130 units.
Problem 2
A square-shaped building measuring 16900 square feet is built; if each of the sides is √16900, what will be the square feet of half of the building?
8450 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 16900 by 2 = 8450
So half of the building measures 8450 square feet.
Problem 3
Calculate √16900 x 5.
650
Explanation
The first step is to find the square root of 16900, which is 130.
The second step is to multiply 130 by 5.
So 130 x 5 = 650.
Problem 4
What will be the square root of (16900 + 100)?
The square root is 130.38
Explanation
To find the square root, we need to find the sum of (16900 + 100).
16900 + 100 = 17000, and then √17000 ≈ 130.38.
Therefore, the square root of (16900 + 100) is approximately 130.38.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √16900 units and the width ‘w’ is 50 units.
The perimeter of the rectangle is 360 units.
Explanation
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√16900 + 50) = 2 × (130 + 50) = 2 × 180 = 360 units.
FAQ on Square Root of 16900
1.What is √16900 in its simplest form?
2.Mention the factors of 16900.
3.Calculate the square of 16900.
4.Is 16900 a prime number?
5.16900 is divisible by?
Important Glossaries for the Square Root of 16900
- Square root: A square root is the inverse of a square. Example: 1302 = 16900, and the inverse of the square is the square root that is √16900 = 130.
- 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.
- Perfect square: A perfect square is an integer that is the square of an integer. Example: 16900 is a perfect square because it is 1302.
- Prime factorization: The process of expressing a number as a product of its prime factors. Example: The prime factorization of 16900 is 22 x 52 x 132.
- Integer: Integers include all whole numbers and their negatives. Example: -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5 are integers.
Explore More algebra
Previous to Square Root of 16900
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.
