299 LearnersLast updated on May 26th, 2025
Cube Root Of 135
The cube root of a number is a value that when multiplied by itself three times gives back the original number. We apply the function of cube roots in the fields of engineering, designing, financial mathematics, and many more. Let's learn more about the cube root of 135.
What Is The Cube Root Of 135?
The cube root can be classified into two categories: perfect cubes and non-perfect cubes. For example, the cube root of 216 is 6 which is a whole number, making it a perfect cube. However, the cube root of 135 is not a whole number. The cube root of 135 is approximately 5.13.
The cube root of 135 is represented using the radical sign as ∛135, and can also be written in exponential form as 1351/3. The prime factorization of 135 is 33 × 5. It is also an irrational number where ∛135 cannot be expressed in the form of p/q where both p and q are integers and q ≠ 0.
Struggling with Math?
Get 1:1 Coaching to Boost Grades Fast !
Cube Root of 135 by Halley’s Method
Halley’s method is a step-by-step way to find the cube root of a non-perfect cube number. Here, we will find the value of ‘a’ where a3 is the non-perfect cube
∛a≅ x (x3+2a) / (2x3+a) is the formula used in this method.
As 135 is a non-perfect cube number, it lies between the two perfect cube numbers. Here, ‘a’ lies between 125 (53) and 216 (63)
By applying Halley’s Method, we get.
Step 1: Let the number ‘a’ = 135. Start by taking ‘x’ = 5, as 125 (∛125 = 5) is the nearest perfect cube which is closer to 135
Step 2: Apply the value of ‘a = 135’ and ‘x = 5’ in the formula:
∛a≅ x (x3+2a) / (2x3+a)
Step 3: The formula will be,
∛135 ≅ 5 (53+2*135) (2*53+135)
Step 4: After simplifying, we get the cube root of 135 as 5.12992784
Common Mistakes and How to Avoid Them in the Cube Root of 135
Making mistakes while learning cube roots is common. Let’s look at some common mistakes kids might make and how to fix them.
Mistake 1
Incorrect calculation after applying values in the formula
Sometimes instead of using the ‘+’ symbol, kids may accidentally use the multiplication symbol ‘×’. This can lead to wrong calculations and incorrect results. Always double-check the symbols used in the formula to make sure you’re adding, not multiplying, when needed.
Mistake 2
Rounding the number too early
Take the example of ∛135 which is a non-perfect cube number, therefore, the root will not be a whole number. In that case, children round off the number by 2 places of decimal. So the value of the root will be 5.12992784, but by mistake, children write it down as 5.128. For cube root or square root, it is important to find out the real number.
Mistake 3
Not considering negative cube roots
Unlike the square root of a number, here the children should keep in mind that the cube roots of a negative number will always be negative. For example, ∛-216 will be -6.
Mistake 4
Overlooking the decimals in the approximate value
Kids should understand that the cube root of a non-perfect cube will not give a whole number. One should remember that numbers include both perfect and non-perfect cubes. For example, while the cube root of 125 is 5, the cube root of 135 will always be a decimal number. So, always expect decimal numbers for non-perfect cubes.
Mistake 5
Confusion between the Cube of 135 and its Cube Root of 135
The cube of a number is the value when multiplied three times by itself resulting in the original number. For example, the cube of 135 is 135×135×135. Meanwhile, the cube root of a number is the value that, when multiplied three times, gives the original number. For example, the cube root of 135 is 5.13. Students get confused between these two terms as they involve cubes and assume that it's the same.
Level Up with a Math Certification!
2X Faster Learning (Grades 1-12)
Cube Root of 135 Examples
Problem 1
A concrete block has a volume of 135 cubic feet. What is the length of one side of the block if it is cube-shaped?
The side length of the cubic-shaped block is approximately 5.13 feet.
Explanation
To find the side length, take the cube root of 135
∛135 = 5.13 feet
Problem 2
Question: Solve (∛135 × ∛136) and round it to the nearest whole number.
When you solve this, you get 26.3809780329. The nearest whole number is 26.
Explanation
The values of ∛135 and ∛136 are 5.12992784003 and 5.14256318132. Multiplying these will give you the answer 26.3809780329.
Problem 3
A rectangular prism has a volume of 135 cubic inches. If the length and width are both 2 inches. What is the height?
V = V= l × w × h is the volume formula for a rectangular prism.
Solving for h: 135 = 2 × 2 × h
h = 135/4
h = 33.75 inches
Explanation
The height of the rectangular prism is 33.75 inches.
Problem 4
Find ∛4²-3²
The solution to the question is approximately 1.9129.
Explanation
First you need to calculate the numbers inside.
Turn your child into a math star!
#1 Math Hack Schools Won't Teach!
FAQs For Cube Root Of 135
1.What will be the cube of 12?
2.What does ∛27 mean?
3.How to find a cube root?
4.What is the square of a number?
5.So, what is the square root of (-2)?
6.How does learning Algebra help students in Saudi Arabia make better decisions in daily life?
7.How can cultural or local activities in Saudi Arabia support learning Algebra topics such as Cube Root Of 135 ?
8.How do technology and digital tools in Saudi Arabia support learning Algebra and Cube Root Of 135 ?
9.Does learning Algebra support future career opportunities for students in Saudi Arabia?
Struggling with Math?
Get 1:1 Coaching to Boost Grades Fast !
Important Glossaries for Cube Root Of 135
- Fraction: It is a way to show a part of something. For example, in the fraction 25 , it means you have 2 out of 5 equal parts.
- Exponent: It is a smaller number that shows us how many times we multiply the number by itself. For example, in 33, 3 is the exponent, which means we multiply 3 three times.
- Decimal: A number that includes a whole part and a fractional part, which is separated by a dot (.) like 0.5, 3.14, etc.,
- Perfect cube: A number that can be expressed as the product of a whole number multiplied by itself three times, like the cube root of 8 is 2 which is a perfect cube. However, the number cannot be expressed as a whole number when finding its cube root, a non-perfect cube like 135.
- Irrational Number: These are real numbers but cannot be expressed in the form of p/q where both p and q are integers and q ≠ 0.
Explore More algebra
![Important Math Links Icon]()
Previous to Cube Root Of 135
About BrightChamps in Saudi Arabia
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.
