104 LearnersLast updated on May 26th, 2025
Square Root of 9801
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 9801.
What is the Square Root of 9801?
The square root is the inverse of the square of the number. 9801 is a perfect square. The square root of 9801 is expressed in both radical and exponential form. In the radical form, it is expressed as √9801, whereas (9801)^(1/2) in the exponential form. √9801 = 99, 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 9801
The prime factorization method is used for perfect square numbers. Here, we will use the prime factorization method to find the square root of 9801.
- Prime factorization method
Square Root of 9801 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 9801 is broken down into its prime factors.
Step 1: Finding the prime factors of 9801
Breaking it down, we get 3 × 3 × 1089, and 1089 = 3 × 3 × 121, and 121 = 11 × 11. Thus, 9801 = 3 × 3 × 3 × 3 × 11 × 11.
Step 2: Now we found out the prime factors of 9801. The next step is to make pairs of those prime factors: (3, 3), (3, 3), and (11, 11). Since 9801 is a perfect square, we can pair the factors. Therefore, calculating 9801 using prime factorization, we get √9801 = 3 × 3 × 11 = 99.
Square Root of 9801 by Long Division Method
The long division method is particularly used for non-perfect square numbers. However, it can also be applied to perfect squares for verification. Here is how you can find the square root using the long division method:
Step 1: Pair the digits of 9801 starting from the right: 98 and 01.
Step 2: Find the largest number whose square is less than or equal to 98. Here, it is 9, as 9 × 9 = 81.
Step 3: Subtract 81 from 98 to get the remainder 17. Bring down the next pair, 01, to get 1701.
Step 4: Double the quotient obtained so far (9) to get 18, and find a digit n such that 18n × n ≤ 1701.
Step 5: n is 9 here, since 189 × 9 = 1701.
Step 6: Subtracting 1701 from 1701 leaves a remainder of 0. The quotient obtained is 99.
So, the square root of √9801 is 99.
Square Root of 9801 by Approximation Method
Since 9801 is a perfect square, the approximation method is not needed. However, if it were not, this method could be useful for finding square roots to a certain degree of accuracy.
Step 1: Identify the perfect squares closest to 9801. The closest are 9604 (98^2) and 10000 (100^2). Since 9801 is exactly 99^2, the approximation method confirms the exactness.
Common Mistakes and How to Avoid Them in the Square Root of 9801
Students make mistakes while finding the square root, such as forgetting about the negative square root and 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 often focus on the positive square root, as it is the required one in most cases.
For example: √9801 = 99, but there is also -99 which should not be forgotten.
Square Root of 9801 Examples
Problem 1
Can you help Max find the side length of a square if its area is given as 9801 square units?
The side length of the square is 99 units.
Explanation
The side length of the square = √area.
The area is given as 9801 square units.
Side length = √9801 = 99.
Therefore, the side length of the square is 99 units.
Problem 2
A square-shaped garden measuring 9801 square feet is built. If each of the sides is √9801, what will be the square feet of half of the garden?
4900.5 square feet
Explanation
We can divide the given area by 2 as the garden is square-shaped.
Dividing 9801 by 2, we get 4900.5.
So half of the garden measures 4900.5 square feet.
Problem 3
Calculate √9801 × 5.
495
Explanation
The first step is to find the square root of 9801, which is 99.
The second step is to multiply 99 with 5.
So, 99 × 5 = 495.
Problem 4
What will be the square root of (9801 + 0)?
The square root is 99.
Explanation
To find the square root, we need to find the sum of (9801 + 0). 9801 + 0 = 9801, and then √9801 = 99.
Therefore, the square root of (9801 + 0) is ±99.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √9801 units and the width ‘w’ is 20 units.
We find the perimeter of the rectangle as 238 units.
Explanation
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√9801 + 20) = 2 × (99 + 20) = 2 × 119 = 238 units.
FAQ on Square Root of 9801
1.What is √9801 in its simplest form?
2.Mention the factors of 9801.
3.Calculate the square of 99.
4.Is 9801 a prime number?
5.9801 is divisible by?
6.How does learning Algebra help students in Qatar make better decisions in daily life?
7.How can cultural or local activities in Qatar support learning Algebra topics such as Square Root of 9801?
8.How do technology and digital tools in Qatar support learning Algebra and Square Root of 9801?
9.Does learning Algebra support future career opportunities for students in Qatar?
Important Glossaries for the Square Root of 9801
- Square root: A square root is the inverse of a square. Example: 10^2 = 100, and the inverse of the square is the square root, that is, √100 = 10.
- Rational number: A rational number can be expressed 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: 81 is a perfect square because it is 9^2.
- Long division method: A mathematical method used to find the square root of a number through successive division.
- Prime factorization: The process of expressing a number as the product of its prime factors.
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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.
