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 4/9.
The square root is the inverse of the square of the number. The square root of 4/9 can be expressed in both radical and exponential forms. In the radical form, it is expressed as √(4/9), whereas in the exponential form, it is expressed as (4/9)^(1/2). The square root of 4/9 is 2/3, 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 square root of a fraction can be found by taking the square roots of the numerator and the denominator separately. Let us now learn how to do this:
1. Find the square root of the numerator.
2. Find the square root of the denominator.
The prime factorization method is used for perfect squares. The number 4 is a perfect square, and 9 is also a perfect square. Let's find their square roots:
Step 1: Find the prime factors of 4 and 9. - 4 = 2 x 2 = 2^2 - 9 = 3 x 3 = 3^2
Step 2: Take the square root of each: - √4 = 2 - √9 = 3 Step 3: Combine the roots: - √(4/9) = 2/3
The long division method is typically used for non-perfect square numbers, but since both the numerator and the denominator of 4/9 are perfect squares, we can directly find their roots. However, let's apply it briefly:
Step 1: Identify the square roots of 4 and 9 separately: - √4 = 2 - √9 = 3
Step 2: Combine the results: - √(4/9) = 2/3
Approximation is not needed in this case since both the numerator and the denominator are perfect squares. However, if you were to estimate, it would directly lead to the exact answer due to their simplicity:
Step 1: Recognize the perfect squares: - The smallest perfect square greater than 4 is 4 itself, and the same applies for 9.
Step 2: Determine: - √4 = 2 - √9 = 3 Thus, √(4/9) = 2/3.
Students often make mistakes while finding the square root, such as forgetting about the negative square root or mishandling fractions. Now, let us look at a few of those mistakes in detail.
Can you help Max find the side length of a square box if its area is given as 4/9 square units?
The side length of the square is 2/3 units.
The side length of a square can be found by taking the square root of its area. Since the area is 4/9, the side length is √(4/9) = 2/3 units.
A square-shaped plot measures 4/9 square meters. What will be the area of half of the plot?
2/9 square meters
We can just divide the given area by 2 to find half of the plot. Dividing 4/9 by 2 gives us 2/9.
Calculate 5 x √(4/9).
10/3
First, find the square root of 4/9, which is 2/3. Then multiply it by 5: 5 x (2/3) = 10/3.
What is the square root of (4/9 + 1/9)?
The square root is 1.
First, find the sum of (4/9 + 1/9), which is 5/9.
Then find the square root of 5/9, which simplifies to √5/3.
Since it does not simplify further, there is no exact integer square root.
Find the perimeter of a rectangle if its length ‘l’ is √(4/9) units and the width ‘w’ is 3 units.
The perimeter of the rectangle is 8 units.
Perimeter of the rectangle = 2 × (length + width).
Thus, Perimeter = 2 × (2/3 + 3)
= 2 × (11/3)
= 22/3
= 8 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.