122 LearnersLast updated on May 26th, 2025
Square Root of 25/9
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 25/9.
What is the Square Root of 25/9?
The square root is the inverse of the square of the number. 25/9 is a perfect square fraction. The square root of 25/9 is expressed in both radical and exponential form. In the radical form, it is expressed as √(25/9), whereas (25/9)^(1/2) in the exponential form. √(25/9) = 5/3, 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 25/9
The prime factorization method is used for perfect square numbers. However, for perfect square fractions like 25/9, we can find the square root by taking the square root of both the numerator and the denominator separately. Let us now learn the following methods:
- Prime factorization method
- Simplification method
Square Root of 25/9 by Prime Factorization Method
The product of prime factors is the Prime factorization of a number. Now let us look at how 25 and 9 are broken down into their prime factors:
Step 1: Finding the prime factors of 25 and 9 - 25 can be broken down as 5 x 5: 5² - 9 can be broken down as 3 x 3: 3²
Step 2: Since both 25 and 9 are perfect squares, we can easily find the square root of each.
Thus, √(25/9) = √25/√9 = 5/3.
Square Root of 25/9 by Simplification Method
The simplification method involves simplifying the given fraction and then finding the square root.
Step 1: The fraction 25/9 is already in its simplest form.
Step 2: Find the square root of the numerator and the denominator separately: √25 = 5 and √9 = 3.
Step 3: Therefore, √(25/9) = 5/3.
Common Mistakes and How to Avoid Them in the Square Root of 25/9
Students do make mistakes while finding the square root, such as forgetting about the negative square root or confusing square roots with cube roots. 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 typically consider only the positive square root, as it is the principal root.
For example, √(25/9) = 5/3, but there is also -5/3.
Mistake 2
Not adding square root symbol in proper places
Not using the square root symbol 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, √(25/9) should not be confused with (√25/√9) = 5/3.
Mistake 3
Not finding the correct value of a non-perfect square
While 25/9 is a perfect square fraction, it's crucial to simplify and correctly identify the value.
For example, √(50/4) is not an integer, but students must understand the simplification process.
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 avoid mistakes.
For example, √(25/9) and ∛(25/9) are different.
Mistake 5
Making mistakes in simplification
Finding a square root using simplification involves basic arithmetic operations. Students may skip steps or miscalculate, leading to errors. It's important to follow the steps methodically.
Square Root of 25/9 Examples
Problem 1
Can you help Max find the side length of a square box if its area is given as 25/9 square units?
The side length of the square is 5/3 units.
Explanation
The side length of the square = √(area).
The area is given as 25/9 square units.
Side length of the square = √(25/9)
= 5/3 units.
Problem 2
A rectangular garden has an area of 25/9 square meters. If the width is 1/3 meters, what is the length?
The length of the garden is 5 meters.
Explanation
Area of the rectangle = length × width.
Given the area is 25/9 and the width is 1/3 meters.
Length = (Area/Width)
= (25/9) ÷ (1/3)
= (25/9) × (3/1)
= 25/3
= 5 meters.
Problem 3
Calculate √(25/9) × 4.
20/3
Explanation
The first step is to find the square root of 25/9, which is 5/3.
The second step is to multiply 5/3 by 4.
So, (5/3) × 4 = 20/3.
Problem 4
What will be the square root of (16 + 9)?
The square root is 5.
Explanation
To find the square root, we need to find the sum of (16 + 9).
16 + 9 = 25, and then √25 = 5.
Therefore, the square root of (16 + 9) is ±5.
Problem 5
Find the perimeter of a rectangle if its length 'l' is √(25/9) units and the width 'w' is 3 units.
The perimeter of the rectangle is 16 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√(25/9) + 3)
= 2 × (5/3 + 3)
= 2 × (5/3 + 9/3)
= 2 × 14/3
= 28/3
= 16 units.
FAQ on Square Root of 25/9
1.What is √(25/9) in its simplest form?
2.Mention the factors of 25/9.
3.Calculate the square of 25/9.
4.Is 25/9 a prime fraction?
5.25/9 is divisible by?
6.How does learning Algebra help students in Indonesia make better decisions in daily life?
7.How can cultural or local activities in Indonesia support learning Algebra topics such as Square Root of 25/9?
8.How do technology and digital tools in Indonesia support learning Algebra and Square Root of 25/9?
9.Does learning Algebra support future career opportunities for students in Indonesia?
Important Glossaries for the Square Root of 25/9
- Square root: A square root is the inverse operation to squaring a number. For example, 4² = 16, and the inverse of the square is the square root, √16 = 4.
- 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.
- Principal square root: The principal square root is the positive square root of a number. For example, the principal square root of 9 is 3.
- Perfect square: A perfect square is a number that can be expressed as the square of an integer. For example, 25 is a perfect square because it is 5².
- Fraction: A fraction is a numerical quantity that is not a whole number, representing a part of a whole. It is expressed as a ratio of two numbers, such as 5/3.
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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
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