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, finance, etc. Here, we will discuss the square root of 1/64.
The square root is the inverse of the square of a number. 1/64 is a perfect square. The square root of 1/64 can be expressed in both radical and exponential form. In the radical form, it is expressed as √(1/64), whereas (1/64)^(1/2) is the exponential form. √(1/64) = 1/8, 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 is often used. However, since 1/64 is already a perfect square, we can find its square root directly using the following methods:
Since 1/64 is a perfect square, we can find its square root directly:
Step 1: Recognize that 1/64 can be rewritten as (1/8)².
Step 2: The square root of (1/8)² is simply 1/8. Therefore, √(1/64) = 1/8.
The prime factorization method involves expressing the number as a product of prime numbers. Since 1 is already a perfect square, we focus on 64:
Step 1: Find the prime factors of 64. Breaking it down, we get 2 x 2 x 2 x 2 x 2 x 2 = 2^6.
Step 2: The prime factorization of 64 is 2^6. The square root of 64 is found by halving the exponent of the prime factors: √(2^6) = 2^3 = 8.
Step 3: Therefore, √(1/64) = 1/√64 = 1/8.
Students do sometimes make mistakes while finding the square root, such as forgetting about negative square roots or misapplying methods. Let's look at a few of these mistakes in detail.
Students do make mistakes while finding the square root, such as forgetting about the negative square root or skipping proper simplification methods. Let's look at a few of these mistakes in detail.
Can you help Max find the area of a square box if its side length is given as √(1/64)?
The area of the square is 1/64 square units.
The area of a square = side².
The side length is given as √(1/64).
Area of the square = side² = (1/8) x (1/8) = 1/64.
Therefore, the area of the square box is 1/64 square units.
A square-shaped building measuring 1/64 square feet is built; if each of the sides is √(1/64), what will be the square feet of half of the building?
1/128 square feet
We can just divide the given area by 2 as the building is square-shaped.
Dividing 1/64 by 2 = 1/128.
So half of the building measures 1/128 square feet.
Calculate √(1/64) x 5.
5/8
The first step is to find the square root of 1/64, which is 1/8.
The second step is to multiply 1/8 by 5.
So, (1/8) x 5 = 5/8.
What will be the square root of (1/64 + 1/64)?
The square root is 1/4.
To find the square root, we need to find the sum of (1/64 + 1/64).
1/64 + 1/64 = 2/64 = 1/32, and then √(1/32) = 1/√32 ≈ 1/5.65685 = 1/4 (approximately).
Therefore, the square root of (1/64 + 1/64) is approximately 1/4.
Find the perimeter of a rectangle if its length 'l' is √(1/64) units and the width 'w' is 1/4 units.
The perimeter of the rectangle is 3/4 units.
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√(1/64) + 1/4) = 2 × (1/8 + 1/4) = 2 × (1/8 + 2/8) = 2 × (3/8) = 6/8 = 3/4 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.