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 9/5.
The square root is the inverse of the square of the number. 9/5 is not a perfect square. The square root of 9/5 is expressed in both radical and exponential form. In radical form, it is expressed as √(9/5), whereas (9/5)^(1/2) in exponential form. √(9/5) = √9/√5 = 3/√5 = 3√5/5, 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.
The prime factorization method is used for perfect square numbers. However, the prime factorization method is not used for non-perfect square numbers such as fractions, where rationalizing the denominator is often used. Let us now learn the following methods:
Rationalizing the denominator involves converting a fraction with a square root in the denominator into an equivalent fraction with a rational denominator.
Step 1: Identify the square root in the denominator. Here, it is √5.
Step 2: Multiply both the numerator and the denominator by √5 to eliminate the square root from the denominator. (3/√5) × (√5/√5) = (3√5)/5
Step 3: Now, the expression is rationalized, with the square root remaining only in the numerator.
Decimal approximation is another method for finding square roots, and it is useful for estimating the value.
Step 1: Calculate the decimal form of 9/5, which is 1.8.
Step 2: Find the square root of 1.8 using a calculator or estimation, which is approximately 1.3416.
Students often make mistakes when working with square roots, especially with fractions. Here are some common mistakes and how to avoid them:
When dealing with square roots of fractions, it's crucial to rationalize the denominator.For instance, leaving the answer as 3/√5 without rationalizing would be incorrect in some contexts. Always multiply by the conjugate to rationalize.
Students do make mistakes while finding the square root, like forgetting to rationalize the denominator or ignoring the negative square root. Skipping steps in calculation can also lead to errors. Now let us look at a few of those mistakes that students tend to make in detail.
Can you help Max find the area of a square if its side length is given as √(9/5)?
The area of the square is approximately 1.8 square units.
The area of the square = side².
The side length is given as √(9/5).
Area of the square = side²
= (√(9/5))²
= 9/5
= 1.8.
Therefore, the area of the square is 1.8 square units.
A square-shaped park measuring 9/5 square units is created. If each of the sides is √(9/5), what will be the total length of the boundary of the park?
Approximately 5.3664 units.
The perimeter of a square = 4 × side.
Side length = √(9/5)
≈ 1.3416.
Perimeter = 4 × 1.3416
≈ 5.3664 units.
Calculate √(9/5) × 10.
Approximately 13.416.
First, find the square root of 9/5, which is approximately 1.3416.
Then, multiply 1.3416 by 10.
So, 1.3416 × 10 ≈ 13.416.
What will be the square root of (45/25)?
The square root is 3/5.
To find the square root, we need to simplify (45/25) to (9/5).
Then, √(9/5) = 3/√5 = 3√5/5.
Therefore, the square root of (45/25) is 3/5.
Find the perimeter of the rectangle if its length ‘l’ is √(9/5) units and the width ‘w’ is 5 units.
The perimeter of the rectangle is approximately 12.6832 units.
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√(9/5) + 5)
Perimeter = 2 × (1.3416 + 5)
Perimeter ≈ 2 × 6.3416
≈ 12.6832 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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