Last updated on May 26th, 2025
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.
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.
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:
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.
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.
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.
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.
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.
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.
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
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.
Calculate √(100/9) x 5.
50/3 or approximately 16.6667
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.
What will be the square root of (81/4 + 19/4)?
The square root is 5.
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.
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.
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.
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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