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 64/121.
The square root is the inverse of the square of the number. The fraction 64/121 can be expressed as a perfect square. The square root of 64/121 is expressed in both radical and exponential forms. In radical form, it is expressed as √(64/121), whereas (64/121)^(1/2) is in the exponential form. √(64/121) = 8/11, 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. Since 64/121 is a perfect square, we can use prime factorization, along with other methods if necessary. 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 64 and 121 are broken down into their prime factors.
Step 1: Finding the prime factors of 64 and 121.
Step 2: Now that we found the prime factors, we can take the square root of each part. √(64/121) = √(2^6)/√(11^2) = (2^3)/(11) = 8/11.
The simplification method is a straightforward way to find the square root of a fraction if both numerator and denominator are perfect squares.
Step 1: Identify the square roots of the numerator and the denominator separately.
Step 2: Divide the square root of the numerator by the square root of the denominator.
So, √(64/121) = 8/11.
Verification is another way to ensure that the calculation is correct.
Step 1: Multiply the result by itself to see if it equals the original fraction. (8/11) x (8/11) = 64/121.
Step 2: Since this equals the original fraction, the square root calculation is verified.
Students make mistakes while finding the square root, such as misunderstanding fractions and skipping steps in simplification. 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 box if its side length is given as √(64/121)?
The area of the square is 64/121 square units.
The area of the square = side^2.
The side length is given as √(64/121).
Area of the square = side^2 = (8/11) x (8/11) = 64/121.
Therefore, the area of the square box is 64/121 square units.
A square-shaped building measuring 64/121 square feet is built; if each of the sides is √(64/121), what will be the square feet of half of the building?
32/121 square feet
We can just divide the given area by 2 as the building is square-shaped.
Dividing 64/121 by 2 = 32/121.
So half of the building measures 32/121 square feet.
Calculate √(64/121) x 5.
40/11
The first step is to find the square root of 64/121, which is 8/11, the second step is to multiply 8/11 by 5.
So, (8/11) x 5 = 40/11.
What will be the square root of (64/121 + 1)?
The square root is 12/11.
To find the square root, we need to find the sum of (64/121 + 1). 64/121 + 121/121 = 185/121.
Now, √(185/121) = √185/√121 = √185/11.
Since 185 is not a perfect square, we approximate it.
The approximate square root is around 12/11.
Find the perimeter of the rectangle if its length ‘l’ is √(64/121) units and the width ‘w’ is 3 units.
We find the perimeter of the rectangle as 70/11 units.
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (8/11 + 3) = 2 × (8/11 + 33/11) = 2 × 41/11 = 82/11 = 70/11 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.