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106 LearnersLast updated on March 20th, 2025
Square Root of 99.9
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 like vehicle design, finance, etc. Here, we will discuss the square root of 99.9.
What is the Square Root of 99.9?
The square root is the inverse of the square of the number. 99.9 is not a perfect square. The square root of 99.9 is expressed in both radical and exponential form.
In the radical form, it is expressed as โ99.9, whereas (99.9)(1/2) in exponential form. โ99.9 โ 9.994998749, which is an irrational number because it cannot be expressed in the form of p/q, where p and q are integers and q โ 0.
Finding the Square Root of 99.9
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 99.9 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 99.9 is broken down into its prime factors.
Step 1: Finding the prime factors of 99.9 Breaking it down, we get 2 x 3 x 3 x 5 x 5 x 11.1: 2^1 x 3^2 x 5^2 x 11.1^1
Step 2: Now we found out the prime factors of 99.9. The second step is to make pairs of those prime factors. Since 99.9 is not a perfect square, therefore the digits of the number canโt be grouped in pairs.
Therefore, calculating 99.9 using prime factorization is not straightforward.
Square Root of 99.9 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 99.9, we need to first consider 99 and 0.9.
Step 2: Now we need to find n whose square is less than or equal to 99. We can say n is โ9โ because 9 x 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 90, which is the new dividend (considering 0.9 as 90 for decimal adjustment). Add the old divisor with the same number 9 + 9, we get 18, which will be our new divisor.
Step 4: We now need to find a digit, say โm', such that 18m x m is less than or equal to 1890. After calculation, 189 x 9 = 1701.
Step 5: Subtract 1701 from 1890; the difference is 189, and the quotient is 9.9
Step 6: Since the dividend is less than the divisor, we need to add another decimal point. Adding the decimal point allows us to add two zeroes to the dividend. Now the new dividend is 18900.
Step 7: Continue the process to get more decimal places as needed. Thus, the square root of โ99.9 โ 9.994998749.
Square Root of 99.9 by Approximation Method
The approximation method is another method for finding the square roots, and 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 99.9 using the approximation method.
Step 1: Now we have to find the closest perfect square of โ99.9. The smallest perfect square less than 99.9 is 81, and the largest perfect square greater than 99.9 is 100. โ99.9 falls somewhere between 9 and 10.
Step 2: Now we need to apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Using the formula: (99.9 - 81) / (100 - 81) = 18.9 / 19 = 0.994736842.
Adding this decimal to 9 (the integer part), we get 9 + 0.994736842 โ 9.994998749, so the square root of 99.9 is approximately 9.995.
Common Mistakes and How to Avoid Them in the Square Root of 99.9
Students do make mistakes while finding the square root, like 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: โ50 = 7.07, there is also -7.07 which should not be forgotten.
Square root of 99.9 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as โ99.9?
The area of the square is approximately 998.0005 square units.
Explanation
The area of the square = side2.
The side length is given as โ99.9.
Area of the square = side2 = โ99.9 x โ99.9 โ 9.995 ร 9.995 โ 99.90005 square units.
Therefore, the area of the square box is approximately 99.90005 square units.
Problem 2
A square-shaped building measuring 99.9 square feet is built; if each of the sides is โ99.9, what will be the square feet of half of the building?
49.95 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 99.9 by 2 = we get 49.95.
So half of the building measures 49.95 square feet.
Problem 3
Calculate โ99.9 x 5.
Approximately 49.975
Explanation
The first step is to find the square root of 99.9, which is approximately 9.995.
The second step is to multiply 9.995 by 5. So 9.995 x 5 โ 49.975.
Problem 4
What will be the square root of (89.9 + 10)?
The square root is 10
Explanation
To find the square root, we need to find the sum of (89.9 + 10). 89.9 + 10 = 99.9, and then โ99.9 โ 9.995.
Therefore, the square root of (89.9 + 10) is approximately ยฑ9.995.
Problem 5
Find the perimeter of the rectangle if its length โlโ is โ99.9 units and the width โwโ is 20 units.
We find the perimeter of the rectangle as approximately 59.99 units.
Explanation
Perimeter of the rectangle = 2 ร (length + width).
Perimeter = 2 ร (โ99.9 + 20) โ 2 ร (9.995 + 20) = 2 ร 29.995 โ 59.99 units.
FAQ on Square Root of 99.9
1.What is โ99.9 in its simplest form?
2.Mention the factors of 99.9.
3.Calculate the square of 99.9.
4.Is 99.9 a prime number?
5.99.9 is divisible by?
Important Glossaries for the Square Root of 99.9
- Square root: A square root is the inverse of squaring a number. Example: 4^2 = 16 and the inverse of the square is the square root, that is โ16 = 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.
- 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. That is the reason it is also known as a principal square root.
- Decimal: If a number has a whole number and a fractional part in a single representation, then it is called a decimal. For example, 7.86, 8.65, and 9.42 are decimals.
- Long division method: A method used to find the square root of numbers, especially non-perfect squares, by dividing and averaging progressively.
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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.
