123 LearnersLast updated on May 26th, 2025
Square Root of 1/64
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.
What is 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.
Finding the Square Root of 1/64
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:
- Direct calculation
- Prime factorization method
Square Root of 1/64 by Direct Calculation
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.
Square Root of 1/64 by Prime Factorization Method
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.
Common Mistakes and How to Avoid Them in the Square Root of 1/64
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.
Common Mistakes and How to Avoid Them in the Square Root of 1/64
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.
Mistake 1
Forgetting about the negative square root
It is important to remember that a number has both positive and negative square roots. However, we generally take the positive square root as it is more commonly used.
For example: √(1/64) = 1/8, but there is also -1/8, which should not be forgotten.
Mistake 2
Not simplifying fractions properly
Another common mistake is not simplifying fractions properly before finding the square root.
For example, not recognizing that 1/64 simplifies to (1/8)² can lead to errors. Simplifying the fraction makes it easier to find the square root.
Mistake 3
Confusing square root with cube root
Students need to be taught the difference between cube root and square root, as this will help them avoid mistakes. For example, √(1/64) and ∛(1/64) are different calculations.
Mistake 4
Ignoring the properties of fractions
It's important to remember that when dealing with fractions, both the numerator and denominator should be considered separately.
For example, √(1/64) = √1/√64 = 1/8.
Mistake 5
Misapplying the prime factorization method
When using prime factorization, ensure that you correctly halve the exponent of the prime factors when finding the square root.
For example, from 2^6, the correct square root is 2^3, not 2^5 or any other value.
Square Root of 1/64 Examples
Problem 1
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.
Explanation
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.
Problem 2
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
Explanation
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.
Problem 3
Calculate √(1/64) x 5.
5/8
Explanation
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.
Problem 4
What will be the square root of (1/64 + 1/64)?
The square root is 1/4.
Explanation
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.
Problem 5
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.
Explanation
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.
FAQ on Square Root of 1/64
1.What is √(1/64) in its simplest form?
2.What are the factors of 64?
3.Calculate the square of 1/8.
4.Is 1/64 a perfect square?
5.Is 64 a prime number?
6.How does learning Algebra help students in United States make better decisions in daily life?
7.How can cultural or local activities in United States support learning Algebra topics such as Square Root of 1/64?
8.How do technology and digital tools in United States support learning Algebra and Square Root of 1/64?
9.Does learning Algebra support future career opportunities for students in United States?
Important Glossaries for the Square Root of 1/64
- Square root: A square root is the inverse of a square. Example: 4² = 16 and the inverse of the square is the square root, that is √16 = 4.
- Perfect square: A perfect square is a number that is the square of an integer. Example: 64 is a perfect square because it is 8².
- Rational number: A rational number is a number that can be written in the form of p/q, where p and q are integers and q is not equal to zero.
- Exponent: An exponent refers to the number that indicates how many times a base is multiplied by itself. Example: In 2^3, 3 is the exponent.
- Fraction: A fraction represents a part of a whole and is expressed as p/q, where p and q are integers and q ≠ 0.
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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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