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 fields such as vehicle design and finance. Here, we will discuss the square root of 49/9.
The square root is the inverse of the square of the number. 49/9 is a perfect square fraction. The square root of 49/9 is expressed in both radical and exponential form. In radical form, it is expressed as √(49/9), whereas in exponential form it is expressed as (49/9)^(1/2). √(49/9) = 7/3, 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.
For perfect square numbers, the prime factorization method can be used. However, since 49/9 is a simple fraction of perfect squares, we can directly find its square root. Let us now learn the following methods:
Since 49 and 9 are both perfect squares, we can find the square root of each separately.
Step 1: Find the square root of the numerator (49). √49 = 7
Step 2: Find the square root of the denominator (9). √9 = 3 Therefore, √(49/9) = 7/3.
We can verify our result by squaring the outcome of the square root to check if it equals the original number.
Step 1: Square the result obtained from the direct method. (7/3)² = 49/9
Step 2: Compare it with the original fraction. Since (7/3)² equals 49/9, our result is verified.
Students often make mistakes while finding the square root, such as confusing the process for non-perfect square numbers or forgetting about negative square roots. Let us look at a few common mistakes in detail.
Students often make mistakes while finding the square root, such as confusing the process for non-perfect square numbers or forgetting about negative square roots. Let us look at a few common mistakes in detail.
Can you help Max find the area of a square box if its side length is given as √(49/9)?
The area of the square is 49/9 square units.
The area of the square = side².
The side length is given as √(49/9).
Area of the square = (7/3) × (7/3) = 49/9.
Therefore, the area of the square box is 49/9 square units.
A square-shaped building measuring 49/9 square feet is built; if each of the sides is √(49/9), what will be the square feet of half of the building?
24.5/9 square feet
We can just divide the given area by 2 as the building is square-shaped.
Dividing 49/9 by 2 = 24.5/9.
So half of the building measures 24.5/9 square feet.
Calculate √(49/9) × 5.
35/3
The first step is to find the square root of 49/9, which is 7/3.
The second step is to multiply 7/3 by 5.
So (7/3) × 5 = 35/3.
What will be the square root of (49/9 + 1)?
The square root is 4/3.
To find the square root, we need to find the sum of (49/9 + 1). 49/9 + 9/9 = 58/9. √(58/9) is not an integer, but if simplified, it falls between 2 and 3.
Since 58 is close to 64, which is a perfect square, we can approximate it as √64/9 = 8/3.
Therefore, the square root of (49/9 + 1) is approximately 4/3.
Find the perimeter of the rectangle if its length ‘l’ is √(49/9) units and the width ‘w’ is 38 units.
We find the perimeter of the rectangle as 84/3 + 76 units.
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (7/3 + 38) = 2 × (84/3 + 114/3) = 2 × 198/3 = 396/3 = 132 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.