Square Root of 1/64
2026-02-28 09:57 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-1-by-64

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Last updated on August 5, 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.

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.

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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.

Problem 1

Can you help Max find the area of a square box if its side length is given as √(1/64)?

Okay, lets begin

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.

Well explained 👍

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?

Okay, lets begin

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.

Well explained 👍

Problem 3

Calculate √(1/64) x 5.

Okay, lets begin

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.

Well explained 👍

Problem 4

What will be the square root of (1/64 + 1/64)?

Okay, lets begin

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.

Well explained 👍

Problem 5

Find the perimeter of a rectangle if its length 'l' is √(1/64) units and the width 'w' is 1/4 units.

Okay, lets begin

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.

Well explained 👍

FAQ on Square Root of 1/64

1.What is √(1/64) in its simplest form?

The simplest form of √(1/64) is 1/8 since 1/64 can be expressed as (1/8)².

2.What are the factors of 64?

Factors of 64 are 1, 2, 4, 8, 16, 32, and 64.

3.Calculate the square of 1/8.

We get the square of 1/8 by multiplying the number by itself: (1/8) x (1/8) = 1/64.

4.Is 1/64 a perfect square?

Yes, 1/64 is a perfect square because it can be expressed as (1/8)².

5.Is 64 a prime number?

No, 64 is not a prime number, as it has more than two factors.

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.

Fun Fact

: He loves to play the quiz with kids through algebra to make kids love it.