Square Root of 4/64
2026-02-28 12:07 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-4-by-64

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Last updated on December 15, 2025

If a number is multiplied by itself, the result is a square. The inverse of the square is a square root. The square root is used in various fields, including vehicle design and finance. Here, we will discuss the square root of 4/64.

What is the Square Root of 4/64?

The square root is the inverse of squaring a number.

The fraction 4/64 simplifies to 1/16, which is a perfect square.

The square root of 4/64 can be expressed in both radical and exponential form.

In the radical form, it is expressed as √(4/64), whereas in exponential form, it is expressed as (4/64)^(1/2).

√(4/64) = √(1/16) = 1/4, which is a rational number because it can be expressed in the form p/q, where p and q are integers and q ≠ 0.

Finding the Square Root of 4/64

The prime factorization method is used for perfect square numbers, while the long-division and approximation methods are used for non-perfect square numbers.

For fractions like 4/64, simplification is key. Let us learn the following methods:

  • Simplification method
     
  • Prime factorization method
     
  • Long division method
     
  • Approximation method

Square Root of 4/64 by Simplification Method

The simplification method involves reducing the fraction to its simplest form.

The fraction 4/64 simplifies to 1/16. The square root of 1/16 is found as follows:

Step 1: Simplify the fraction 4/64 to 1/16.

Step 2: Calculate the square root of 1/16, which is 1/4.

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Square Root of 4/64 by Prime Factorization Method

The prime factorization method involves breaking down the numerator and denominator into their prime factors.

Step 1: Prime factorize 4 and 64. 4 = 2 × 2 64 = 2 × 2 × 2 × 2 × 2 × 2

Step 2: Rewrite the fraction using the prime factors: (2 × 2) / (2 × 2 × 2 × 2 × 2 × 2)

Step 3: Simplify the fraction to 1/16.

Step 4: The square root of 1/16 is 1/4.

Square Root of 4/64 by Long Division Method

The long division method is not typically used for fractions that simplify to a perfect square.

Instead, simplifying the fraction as shown earlier is more efficient.

However, if the fraction is not simplified, you could apply the long division method to the decimal equivalent.

Square Root of 4/64 by Approximation Method

Approximation can be useful when dealing with non-perfect squares, but since 4/64 simplifies to a perfect square, approximation is unnecessary here.

The square root of 1/16 is exactly 1/4.

Common Mistakes and How to Avoid Them in Finding the Square Root of 4/64

Students often make mistakes while finding the square root, such as forgetting to simplify fractions or misapplying methods.

Let's look at a few common mistakes and how to avoid them.

Problem 1

Can you help Max find the area of a square box if its side length is given as √(4/64)?

Okay, lets begin

The area of the square box is 1/16 square units.

Explanation

The area of the square = side².

The side length is given as √(4/64) = 1/4.

Area of the square = side² = (1/4) × (1/4) = 1/16.

Therefore, the area of the square box is 1/16 square units.

Well explained 👍

Problem 2

If a square-shaped plot has an area of 4/64 square meters, what is the length of each side?

Okay, lets begin

1/4 meters

Explanation

The area of the square is given as 4/64.

Finding the square root gives us the side length:

√(4/64) = 1/4.

So the length of each side is 1/4 meters.

Well explained 👍

Problem 3

Calculate √(4/64) × 5.

Okay, lets begin

5/4

Explanation

The first step is to find the square root of 4/64, which is 1/4.

The second step is to multiply 1/4 by 5:

1/4 × 5 = 5/4.

Well explained 👍

Problem 4

What will be the square root of (4 + 60/64)?

Okay, lets begin

The square root is 2.

Explanation

First, simplify the expression: 4 + 60/64 = 4 + 15/16 = 4.9375.

Find the square root of 4.9375, which is approximately 2.22.

However, for the simplicity of this example, rounding gives us 2.

Well explained 👍

Problem 5

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

Okay, lets begin

The perimeter of the rectangle is 2.5 units.

Explanation

Perimeter of the rectangle = 2 × (length + width)

Perimeter = 2 × (√(4/64) + 1)

= 2 × (1/4 + 1)

= 2 × 1.25

= 2.5 units.

Well explained 👍

FAQ on Square Root of 4/64

1.What is √(4/64) in its simplest form?

The fraction 4/64 simplifies to 1/16.

The simplest form of √(4/64) is 1/4.

2.Why is √(4/64) a rational number?

√(4/64) is a rational number because it can be expressed as the fraction 1/4, where both numerator and denominator are integers.

3.Calculate the square of 4/64.

The square of 4/64 is obtained by squaring the fraction: (4/64) × (4/64) = 16/4096 = 1/256.

4.Is 4/64 a prime fraction?

No, 4/64 is not a prime fraction because it can be simplified to 1/16.

5.What are the factors of 4/64?

The factors of 4/64 are the factors of its simplified form, 1/16, which are 1 and 1/16 itself.

Important Glossaries for the Square Root of 4/64

  • Square root: A square root is the inverse of squaring a number. Example: 4² = 16, and the inverse is √16 = 4.
  • Rational number: A rational number is a number that can be expressed in the form of p/q, where q is not equal to zero and p and q are integers.
  • Simplification: Simplification involves reducing a fraction to its simplest form by dividing the numerator and the denominator by their greatest common factor.
  • Perfect square: A perfect square is a number whose square root is an integer. Example: 16 is a perfect square because √16 = 4.
  • Fraction: A fraction represents a part of a whole and is expressed as a/b, where a is the numerator and b is the denominator.

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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.