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 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.
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:
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.
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.
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.
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.
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.
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.
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.
Calculate √(25/9) × 4.
20/3
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.
What will be the square root of (16 + 9)?
The square root is 5.
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.
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.
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.
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.
: He loves to play the quiz with kids through algebra to make kids love it.