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474 LearnersLast updated on August 5, 2025
Cube Root of 27/64
What is the Cube Root of 27/64?
We have learned the definition of the cube root. Now, let’s learn how it is represented using a symbol and exponent. The symbol we use to express the cube root is the radical sign (∛), and the exponent we use is ⅓.
In exponential form, ∛(27/64) is written as (27/64)(1/3). The cube root is just the opposite operation of finding the cube of a number. For example: Assume ‘y’ as the cube root of 27/64, then y³ can be 27/64. Since 27/64 is a perfect cube, its cube root is exactly 3/4.
Finding the Cube Root of 27/64
Finding the cube root of a number is to identify the number that must be multiplied three times resulting in the target number. Now, we will go through the different ways to find the cube root of 27/64. The common methods we follow to find the cube root are given below:
- Prime factorization method
- Exact calculation method
Using the properties of fractions Since 27/64 is a perfect cube, we can find its cube root exactly by either using the cube root of the numerator and the denominator separately or using properties of fractions.
Cube Root of 27/64 by Exact Calculation
Let's find the cube root of 27/64 using exact calculation:
The cube root of a fraction is the cube root of the numerator divided by the cube root of the denominator.
∛(27/64) = ∛27 / ∛64 ∛27 = 3 (Since 3³ = 27 ∛64 = 4 and 4³ = 64)
Therefore, ∛(27/64) = 3/4
The cube root of 27/64 is exactly 3/4.
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Common Mistakes and How to Avoid Them in the Cube Root of 27/64
Finding the cube root of a fraction without any errors can be a difficult task for students. This happens for many reasons. Here are a few mistakes the students commonly make and the ways to avoid them:
Mistake 1
Trying to find cube roots without understanding fraction properties.
Students might confuse how to handle cube roots of fractions. They should remember to apply the cube root to both the numerator and the denominator separately.
For example, for 27/64, ∛27 is 3 and ∛64 is 4, leading to the cube root 3/4.
Mistake 2
Ignoring the exponent form
Most of us might forget the fact that cube root can also be written in exponent form.
For example: Forgetting that the cube root of 27/64 is written as (27/64)(1/3). To avoid this error, always learn the forms in which we can express the cube root of a number.
Mistake 3
Confusing cube root with division
Some students might mistakenly assume the cube root of 27/64 involves division by 3. To avoid this, remember that taking the cube root involves finding a number that, when multiplied by itself three times, equals the original number.
Mistake 4
Using incorrect methods for perfect cubes
Instead of using the exact calculation method for perfect cubes like 27/64, students might try more complicated methods. Remember that for perfect cubes, you can directly calculate the cube root of the numerator and denominator separately.
Mistake 5
Rounding too early
Rounding the cube root too early in the process can lead to errors in the subsequent steps.
For example, rounding the cube root of 27/64 to a decimal too soon can cause errors. To avoid this, use exact values for calculations when possible.
Cube Root of 27/64 Examples:
Problem 1
Imagine you have a cube-shaped container that has a total volume of 27/64 cubic meters. Find the length of one side of the container.
Side of the cube = ∛(27/64) = 3/4 meters
Explanation
To find the side of the cube, we need to find the cube root of the given volume.
Therefore, the side length of the cube is exactly 3/4 meters.
Problem 2
A company uses 27/64 cubic meters of a chemical solution. Calculate the amount of solution left after using 1/4 cubic meter.
The amount of solution left is 7/64 cubic meters.
Explanation
To find the remaining solution, subtract the used amount from the total:
27/64 - 1/4 = 27/64 - 16/64 = 11/64 cubic meters.
Problem 3
A bottle holds 27/64 cubic meters of liquid. Another bottle holds a volume of 1/8 cubic meters. What would be the total volume if the bottles are combined?
The total volume of the combined bottles is 11/16 cubic meters.
Explanation
Let’s add the volume of both bottles: 27/64 + 8/64 = 35/64 = 11/16 cubic meters.
Problem 4
When the cube root of 27/64 is multiplied by 2, calculate the resultant value. How will this affect the cube of the new value?
2 × 3/4 = 3/2
The cube of 3/2 = 27/8
Explanation
When we multiply the cube root of 27/64 by 2, it results in a significant change because the cube of the new value increases the volume exponentially.
Problem 5
Find ∛(54/128).
∛(54/128) = ∛(27/64) = 3/4
Explanation
As shown in the question, ∛(54/128) simplifies by recognizing that both numerator and denominator can relate to 27/64.
Therefore, the cube root becomes 3/4.
FAQs on 27/64 Cube Root
1.Can we find the Cube Root of 27/64 exactly?
2.Why is the Cube Root of 27/64 rational?
3.Is it possible to get the cube root of 27/64 without a calculator?
4.Can we find the cube root of any fraction using prime factorization?
5.Is there any formula to find the cube root of a fraction?
Important Glossaries for Cube Root of 27/64
- Cube root: The number that is multiplied three times by itself to get the given number is the cube root of that number.
- Perfect cube: A number is a perfect cube when it is the product of multiplying a number three times by itself. For example, 3 × 3 × 3 = 27, and 4 × 4 × 4 = 64, so 27/64 is a perfect cube.
- Fraction: A part of a whole, represented as a/b where a is the numerator and b is the denominator.
- Rational number: A number that can be expressed as a fraction a/b, where a and b are integers and b is not zero.
- Radical sign: The symbol used to represent a root, expressed as (∛).
Vikrant Sharma
About the Author
Vikrant Sharma 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.
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