120 LearnersLast updated on May 26th, 2025
Square Root of 100/9
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 the field of vehicle design, finance, etc. Here, we will discuss the square root of 100/9.
What is the Square Root of 100/9?
The square root is the inverse of the square of the number. 100/9 is not a perfect square. The square root of 100/9 is expressed in both radical and exponential form. In the radical form, it is expressed as √(100/9), whereas (100/9)^(1/2) in the exponential form. √(100/9) = 10/3, which simplifies to approximately 3.3333, 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 100/9
The prime factorization method is used for perfect square numbers. However, for fractions, we simplify the numerator and denominator separately. For non-perfect square fractions, the long-division method and approximation method can be used. Let us now learn the following methods:
- Simplification method
- Long division method
- Approximation method
Square Root of 100/9 by Simplification Method
The simplification method involves separating the numerator and denominator and finding the square root of each.
Step 1: Find the square root of the numerator, which is 100. The square root of 100 is 10.
Step 2: Find the square root of the denominator, which is 9. The square root of 9 is 3.
Step 3: Divide the square root of the numerator by the square root of the denominator: 10/3. Therefore, the square root of 100/9 is 10/3 or approximately 3.3333.
Square Root of 100/9 by Long Division Method
The long division method is particularly used for non-perfect square numbers and can also be applied to fractions. In this method, we find the square root of the numerator and denominator separately.
Step 1: Use long division to find the square root of 100, which is 10.
Step 2: Similarly, use long division to find the square root of 9, which is 3.
Step 3: Divide these results to get the square root of the fraction: 10/3 or approximately 3.3333.
Square Root of 100/9 by Approximation Method
The approximation method is useful for estimating square roots. Here’s how to approximate the square root of 100/9.
Step 1: Recognize that 100/9 is a fraction of two perfect squares, so we approximate each separately.
Step 2: Calculate √100 ≈ 10 and √9 ≈ 3.
Step 3: Divide the two approximations to get approximately 3.3333. Thus, the approximate square root of 100/9 is 3.3333.
Common Mistakes and How to Avoid Them in the Square Root of 100/9
Students often make mistakes when finding the square root, such as forgetting about the negative square root or incorrectly simplifying the fraction. Let's look at some common mistakes in detail.
Mistake 1
Forgetting about the negative square root
It is important to remember that a number has both positive and negative square roots. However, we usually consider only the positive square root unless specified otherwise.
For example: √(100/9) = ±10/3.
Mistake 2
Not simplifying fractions before taking the square root
Students often forget to simplify the fraction before finding the square root. Simplifying helps to ensure accurate results.
For example, simplify 100/9 to (10/3)^2 before taking the square root.
Mistake 3
Misapplying the square root to each component of the fraction independently
Always apply the square root to both the numerator and the denominator separately before simplifying the fraction.
For example: √(100/9) = √100 / √9 = 10/3, not (100/9) as a whole.
Mistake 4
Confusing the square root symbol with other operations
Be careful not to confuse the square root symbol with other mathematical operations like division or multiplication. Ensure each step is clearly understood.
Mistake 5
Errors in long division calculation
When using the long division method, ensure all steps are followed correctly to avoid errors. Missteps can lead to incorrect results.
Square Root of 100/9 Examples
Problem 1
Can you help Max find the area of a square box if its side length is √(64/9)?
The area of the square is 64/9 square units.
Explanation
The area of the square = side².
The side length is given as √(64/9).
Area of the square = (√(64/9))² = 64/9.
Therefore, the area of the square box is 64/9 square units.
Problem 2
A square-shaped building measuring 100/9 square feet has sides of √(100/9). What will be the square feet of half of the building?
50/9 square feet
Explanation
Divide the given area by 2 as the building is square-shaped.
Dividing 100/9 by 2 = (100/9) / 2 = 50/9.
So half of the building measures 50/9 square feet.
Problem 3
Calculate √(100/9) x 5.
50/3 or approximately 16.6667
Explanation
First, find the square root of 100/9, which is 10/3.
Then multiply 10/3 by 5.
So (10/3) x 5 = 50/3 or approximately 16.6667.
Problem 4
What will be the square root of (81/4 + 19/4)?
The square root is 5.
Explanation
To find the square root, sum (81/4 + 19/4) = 100/4 = 25. The square root of 25 is 5. Therefore, the square root of (81/4 + 19/4) is ±5.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √(64/9) units and the width ‘w’ is 10 units.
The perimeter of the rectangle is 50/3 + 20 = 86.67 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√(64/9) + 10) = 2 × (8/3 + 10) = 2 × (50/3) = 100/3 or approximately 33.33 units.
FAQ on Square Root of 100/9
1.What is √(100/9) in its simplest form?
2.What are the factors of 100?
3.Calculate the square of 10/3.
4.Is 100/9 a rational number?
5.What is the decimal approximation of √(100/9)?
6.How does learning Algebra help students in India make better decisions in daily life?
7.How can cultural or local activities in India support learning Algebra topics such as Square Root of 100/9?
8.How do technology and digital tools in India support learning Algebra and Square Root of 100/9?
9.Does learning Algebra support future career opportunities for students in India?
Important Glossaries for the Square Root of 100/9
- Square root: A square root is the inverse of a square. For example, if 3² = 9, the square root of 9 is √9 = 3.
- Rational number: A rational number is a number that can be written in the form of p/q, where p and q are integers, and q is not equal to zero.
- Fraction: A fraction represents a part of a whole or, more generally, any number of equal parts. It is expressed as a quotient of two numbers, the numerator and the denominator.
- Approximation: Approximating is finding a value that is close enough to the right answer, usually with some thought or calculation involved.
- Numerator and Denominator: In a fraction, the numerator is the top number, and the denominator is the bottom number. The numerator indicates how many parts are considered, while the denominator indicates the total number of equal parts.
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Jaskaran Singh Saluja
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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.
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