Cube Root Of 135
2026-02-28 17:48 Diff
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Last updated on August 5, 2025

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. 
 

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.
 

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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?

Okay, lets begin

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    

Well explained 👍

Problem 2

Question: Solve (∛135 × ∛136) and round it to the nearest whole number.

Okay, lets begin

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.
 

Well explained 👍

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?

Okay, lets begin

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.
 

Well explained 👍

Problem 4

Find ∛4²-3²

Okay, lets begin

The solution to the question is approximately 1.9129. 
 

Explanation

 First you need to calculate the numbers inside.
 

Well explained 👍

FAQs For Cube Root Of 135

1.What will be the cube of 12?

The cube of 12 is 123 = 12×12×12 = 1728. This represents twelve multiplied by itself three times.
 

2.What does ∛27 mean?

The expression  ∛27 represents a cubic root of 27. When we break it up ∛3x  3x  3 we get 3. So the cube of 27 is 3. 

3.How to find a cube root?

To find the cube root of a number ‘x’, you can use the notation ∛x to express it as x1/3. Both represent the value that, when multiplied by itself three times, equals ‘x’. For example, ∛27 = 271/3 = 3, because 3 x3 x3 = 27. 

4.What is the square of a number?

The square of a number is the result of multiplying the number by itself. In other words, if ‘n’ is a number, its square is n2, which means n x n . For example, the square of 5 is (52 =5 x5) = 25. 
 

5.So, what is the square root of (-2)?

The square root of -2 is an imaginary number because the square root of a negative number involves the imaginary unit ‘i’, where ‘i’ = √ -1, thus√  -2 = i√ 2.

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.

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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.