125 LearnersLast updated on May 26th, 2025
Square Root of 9900
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 9900.
What is the Square Root of 9900?
The square root is the inverse of the square of the number. 9900 is not a perfect square. The square root of 9900 is expressed in both radical and exponential form. In the radical form, it is expressed as √9900, whereas (9900)^(1/2) in the exponential form. √9900 ≈ 99.4987, 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 9900
The prime factorization method is used for perfect square numbers. However, the prime factorization method is not used for non-perfect square numbers where the long-division method and approximation method are used. Let us now learn the following methods:
- Prime factorization method
- Long division method
- Approximation method
Square Root of 9900 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 9900 is broken down into its prime factors.
Step 1: Finding the prime factors of 9900
Breaking it down, we get 2 × 2 × 3 × 3 × 5 × 5 × 11: 2^2 × 3^2 × 5^2 × 11
Step 2: Now we found out the prime factors of 9900. The second step is to make pairs of those prime factors. The square root is found by taking one number from each pair of the same number, which yields: 2 × 3 × 5 × √11 = 30√11
Square Root of 9900 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 9900, we need to group it as 99 and 00.
Step 2: Now we need to find n whose square is less than or equal to 99. We can say n is '9' because 9 × 9 = 81, which is less than 99. Now the quotient is 9, after subtracting 81 from 99, the remainder is 18.
Step 3: Now let us bring down 00, which is the new dividend. Add the old divisor with the same number 9 + 9, we get 18, which will be our new divisor.
Step 4: The new divisor will be the sum of the dividend and quotient. Now we get 18n as the new divisor, we need to find the value of n.
Step 5: The next step is finding 18n × n ≤ 1800. Let us consider n as 9, now 18 × 9 = 162.
Step 6: Subtract 1620 from 1800; the difference is 180, and the quotient is 99.
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 18000.
Step 8: Now we need to find the new divisor; let's consider 189 because 1890 × 9 = 17010.
Step 9: Subtracting 17010 from 18000, we get the result 990.
Step 10: Now the quotient is 99.4.
Step 11: Continue doing these steps until we get two numbers after the decimal point. Suppose if there is no decimal values continue till the remainder is zero.
So the square root of √9900 is approximately 99.50.
Square Root of 9900 by Approximation Method
The approximation method is another method for finding the 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 9900 using the approximation method.
Step 1: Now we have to find the closest perfect square of √9900. The smallest perfect square less than 9900 is 9801, and the largest perfect square more than 9900 is 10000. √9900 falls somewhere between 99 and 100.
Step 2: Now we need to apply the formula that is (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Going by the formula (9900 - 9801) / (10000 - 9801) = 99/199 = 0.4975
Using the formula, we identified the decimal point of our square root. The next step is adding the value we got initially to the decimal number, which is 99 + 0.4975 = 99.4975, so the square root of 9900 is approximately 99.50.
Common Mistakes and How to Avoid Them in the Square Root of 9900
Students do make mistakes while finding the square root, likewise forgetting about the negative square root, skipping long division methods, 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 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: √50 = 7.07, there is also -7.07 which should not be forgotten.
Mistake 2
Not adding the square root symbol in proper places
Not using the square root properly is another mistake that children make. To resolve this, we need to teach children that simplifying the numbers inside the square root is important and then move on to the second step.
For example: √(12+24) = √12 + √24 is the wrong method of using roots. The right way of using roots is √(12+24) = √36.
Mistake 3
Not finding the correct value of a non-perfect square
The first step that needs to be taught to children is to simplify the numbers inside the square root. This is important so that students do not make mistakes while identifying the approximate value.
For example: √50 = 7 is wrong; the correct answer is √50 ≈ 7.071067.
Mistake 4
Confusing the square root symbol with the cube root
Students need to be taught the difference between cube root and square root constantly as this will help them keep away from mistakes.
For example: √50 and ∛50 are different.
Mistake 5
Making mistakes in long division
Finding a square root using the long division method involves many steps. Due to this, many students might skip a step accidentally, which results in a wrong answer at the end of the sum. This may either happen in subtracting or elsewhere.
Square Root of 9900 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √9900?
The area of the square is 9900 square units.
Explanation
The area of the square = side^2.
The side length is given as √9900.
Area of the square = side^2 = √9900 × √9900 = 9900.
Therefore, the area of the square box is 9900 square units.
Problem 2
A square-shaped building measuring 9900 square feet is built; if each of the sides is √9900, what will be the square feet of half of the building?
4950 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 9900 by 2 = we get 4950.
So half of the building measures 4950 square feet.
Problem 3
Calculate √9900 × 5.
497.5
Explanation
The first step is to find the square root of 9900, which is approximately 99.50, the second step is to multiply 99.50 with 5.
So 99.50 × 5 = 497.5.
Problem 4
What will be the square root of (9800 + 100)?
The square root is approximately 99.50.
Explanation
To find the square root, we need to find the sum of (9800 + 100). 9800 + 100 = 9900, and then √9900 ≈ 99.50.
Therefore, the square root of (9800 + 100) is approximately ±99.50.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √9900 units and the width ‘w’ is 100 units.
We find the perimeter of the rectangle as approximately 399 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√9900 + 100) = 2 × (99.50 + 100) = 2 × 199.50 = 399 units.
FAQ on Square Root of 9900
1.What is √9900 in its simplest form?
2.Mention the factors of 9900.
3.Calculate the square of 9900.
4.Is 9900 a prime number?
5.9900 is divisible by?
6.How does learning Algebra help students in Bahrain make better decisions in daily life?
7.How can cultural or local activities in Bahrain support learning Algebra topics such as Square Root of 9900?
8.How do technology and digital tools in Bahrain support learning Algebra and Square Root of 9900?
9.Does learning Algebra support future career opportunities for students in Bahrain?
Important Glossaries for the Square Root of 9900
- Square root: A square root is the inverse of a square. Example: 4^2 = 16 and the inverse of the square is the square root that is √16 = 4.
- Irrational number: An irrational number is a number that cannot be written in the form of p/q, where q is not equal to zero and p and q are integers.
- Prime factorization: The process of expressing a number as the product of its prime factors. For example, the prime factorization of 9900 is 2 × 2 × 3 × 3 × 5 × 5 × 11.
- Perfect square: A perfect square is a number that is the square of an integer. For example, 100 is a perfect square because it is 10^2.
- Exponent: A mathematical notation indicating the number of times a number is multiplied by itself. For example, in 5^3, the exponent is 3, indicating 5 is multiplied by itself three times.
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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.
