126 LearnersLast updated on May 26th, 2025
Square Root of 64/121
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.
What is 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.
Finding the Square Root of 64/121
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:
- Prime factorization method
- Simplification method
- Verification method
Square Root of 64/121 by Prime Factorization Method
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.
- 64 can be broken down as 2 x 2 x 2 x 2 x 2 x 2 (i.e., 2^6).
- 121 can be broken down as 11 x 11 (i.e., 11^2).
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.
Square Root of 64/121 by Simplification Method
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.
- The square root of 64 is 8.
- The square root of 121 is 11.
Step 2: Divide the square root of the numerator by the square root of the denominator.
So, √(64/121) = 8/11.
Verification of the Square Root of 64/121
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.
Common Mistakes and How to Avoid Them in the Square Root of 64/121
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.
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 will be taking only the positive square root, as it is the required one.
For example: √(64/121) = ±8/11, but we typically use the positive value.
Mistake 2
Not simplifying the fraction properly
Not simplifying the fraction properly can lead to incorrect results. Ensure that both the numerator and the denominator are perfect squares before calculating their roots.
Mistake 3
Confusing the square root of a fraction with separate square roots
Some students mistakenly apply the square root separately to non-perfect square fractions.
For example, √(64/121) is not equal to √64/√121 unless both numerator and denominator are perfect squares.
Mistake 4
Mixing up multiplication and division in verification
Students sometimes confuse operations while verifying results. Ensure that the multiplication of the result by itself (8/11 x 8/11) equals the original fraction (64/121).
Mistake 5
Misplacing decimal points in other calculations
While this doesn't apply directly to 64/121, students often misplace decimal points when dealing with other fractions. Always double-check calculations.
Square Root of 64/121 Examples
Problem 1
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.
Explanation
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.
Problem 2
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
Explanation
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.
Problem 3
Calculate √(64/121) x 5.
40/11
Explanation
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.
Problem 4
What will be the square root of (64/121 + 1)?
The square root is 12/11.
Explanation
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.
Problem 5
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.
Explanation
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.
FAQ on Square Root of 64/121
1.What is √(64/121) in its simplest form?
2.Mention the factors of 64 and 121.
3.Calculate the square of 64/121.
4.Is 64/121 a rational number?
5.Is 64/121 a perfect square?
6.How does learning Algebra help students in Australia make better decisions in daily life?
7.How can cultural or local activities in Australia support learning Algebra topics such as Square Root of 64/121?
8.How do technology and digital tools in Australia support learning Algebra and Square Root of 64/121?
9.Does learning Algebra support future career opportunities for students in Australia?
Important Glossaries for the Square Root of 64/121
- Square root: A square root is the inverse of a square. Example: 4^2 = 16, and the inverse of the square is the square root, that is, √16 = 4.
- Rational number: A rational number is a number that can be written in the form of p/q, where q is not equal to zero, and p and q are integers.
- Perfect square: A number that is the square of an integer. Example: 64 and 121 are perfect squares.
- Fraction: A way to represent numbers that are not whole, using a numerator and a denominator. Example: 64/121 is a fraction.
- Prime factorization: The process of expressing a number as the product of its prime factors. Example: 64 = 2^6.
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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.
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