Square Root of 9/64
2026-02-28 12:08 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-9-by-64

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Last updated on December 15, 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 the field of vehicle design, finance, etc. Here, we will discuss the square root of 9/64.

What is the Square Root of 9/64?

The square root is the inverse of the square of the number.

The fraction 9/64 is a perfect square.

The square root of 9/64 is expressed in both radical and exponential form.

In the radical form, it is expressed as √(9/64), whereas (9/64)(1/2) in the exponential form.

√(9/64) = 3/8, 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 9/64

The prime factorization method is used for perfect square numbers like 9/64.

For fractions, we find the square roots of the numerator and the denominator separately.

Let us now learn the following methods:

  • Prime factorization method
  • Simplification method

Square Root of 9/64 by Prime Factorization Method

The prime factorization method involves finding the prime factors for both the numerator and the denominator separately.

Step 1: Finding the prime factors of 9 and 64 - 9 can be broken down into 3 × 3: 3² 

64 can be broken down into 2 × 2 × 2 × 2 × 2 × 2: 2⁶

Step 2: Now we take the square root of the prime factorizations. - √9 = √(3²) = 3 - √64 = √(2⁶) = 2³ = 8

Step 3: The square root of 9/64 is then 3/8, which is a rational number.

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Square Root of 9/64 by Simplification Method

The simplification method is a straightforward way to find the square root of a fraction by taking the square root of the numerator and the denominator individually.

Step 1: Take the square root of the numerator and the denominator. 

  • The numerator is 9, and √9 = 3
  • The denominator is 64, and √64 = 8

Step 2: Combine the results.

Thus, √(9/64) = 3/8

Applications of the Square Root of 9/64

Understanding the square root of a fraction like 9/64 can be useful in various fields such as geometry and algebra.

For example, if a square has an area of 9/64 square units, then the length of each side of the square is 3/8 units.

This can be particularly beneficial in solving problems related to proportions and scaling in design and engineering.

Common Mistakes and How to Avoid Them in the Square Root of 9/64

Students may make mistakes while finding the square root of a fraction, such as not simplifying the fraction first or incorrectly applying the square root to the numerator and denominator separately.

Let us look at a few common mistakes in detail.

Problem 1

Can you help Max find the side length of a square if its area is 9/64 square units?

Okay, lets begin

The side length of the square is 3/8 units.

Explanation

The side length of the square = √(area).

The area is given as 9/64.

Side length = √(9/64) = 3/8

Therefore, the side length of the square is 3/8 units.

Well explained 👍

Problem 2

A rectangle has a length of 3/8 units and a width of 2 units. What is the perimeter of the rectangle?

Okay, lets begin

The perimeter of the rectangle is 5.75 units.

Explanation

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

Perimeter = 2 × (3/8 + 2) = 2 × (0.375 + 2) = 2 × 2.375 = 4.75 units

Well explained 👍

Problem 3

Calculate √(9/64) × 16.

Okay, lets begin

6

Explanation

First, find the square root of 9/64, which is 3/8.

Then multiply 3/8 by 16. (3/8) × 16 = 6

Well explained 👍

Problem 4

What will be the square root of (16/64 + 1/64)?

Okay, lets begin

The square root is 1/2.

Explanation

First, find the sum of (16/64 + 1/64) 16/64 + 1/64 = 17/64 Then find √(17/64) = 1/2.

Therefore, the square root of (16/64 + 1/64) is ±1/2.

Well explained 👍

Problem 5

If a square has a diagonal of length √(18/64), what is the area of the square?

Okay, lets begin

The area of the square is 9/32 square units.

Explanation

The diagonal of a square is √2 times the side length. Let s be the side length.

Then, s√2 = √(18/64).

s = √(18/64) / √2 = √(18/128) = 3/8.

Area = s² = (3/8)² = 9/32 square units.

Well explained 👍

FAQ on Square Root of 9/64

1.What is √(9/64) in its simplest form?

The simplest form of √(9/64) is 3/8, obtained by taking the square root of both the numerator and the denominator separately.

2.Is 9/64 a perfect square?

Yes, 9/64 is a perfect square because both the numerator (9) and the denominator (64) are perfect squares.

3.Calculate the square of 9/64.

We get the square of 9/64 by multiplying the fraction by itself: (9/64) x (9/64) = 81/4096.

4.Is 9/64 a rational number?

Yes, 9/64 is a rational number because it can be expressed as a fraction where both the numerator and the denominator are integers.

5.What are the factors of 64?

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

Important Glossaries for the Square Root of 9/64

  • 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 number that is the square of an integer. Example: 9 is a perfect square because it is 3².
  • Rational number: A number that can be expressed as the quotient of two integers. Example: 1/2 is a rational number.
  • Fraction: A numerical quantity that is not a whole number, represented by two numbers, the numerator and the denominator. Example: 3/4.
  • Principal square root: The non-negative square root of a number. For example, the principal square root of 9 is 3.

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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.