Cube of 152
2026-02-28 09:59 Diff
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Last updated on August 5, 2025

When a number is multiplied by itself thrice, the resultant number is called the cube of a number. Cubing is often used when comparing sizes of objects or things with cubic measurements. In this topic, we shall learn about the cube of 152.

Cube of 152

A cube number is a value obtained by raising a number to the power of 3, or by multiplying the number by itself three times. When you cube a positive number, the result is always positive. When you cube a negative number, the result is always negative. This is because a negative number multiplied by itself three times results in a negative number.

The cube of 152 can be written as 152³, which is the exponential form. Or it can also be written in arithmetic form as, 152 × 152 × 152.

How to Calculate the Value of Cube of 152

To check whether a number is a cube number or not, we can use the following three methods: multiplication method, a factor formula (a³), or by using a calculator. These methods will help students cube numbers faster and easier without feeling confused or stuck while evaluating the answers. -

  1. By Multiplication Method 
  2. Using a Formula 
  3. Using a Calculator

By Multiplication Method

The multiplication method is a process in mathematics used to find the product of numbers or quantities by combining them through repeated addition. It is a fundamental operation that forms the basis for more complex mathematical concepts.

Step 1: Write down the cube of the given number. 152³ = 152 × 152 × 152

Step 2: You get 3,511,808 as the answer. Hence, the cube of 152 is 3,511,808.

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Using a Formula (a³)

The formula (a + b)³ is a binomial formula for finding the cube of a number. The formula is expanded as a³ + 3a²b + 3ab² + b³.

Step 1: Split the number 152 into two parts. Let a = 150 and b = 2, so a + b = 152

Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³

Step 3: Calculate each term

a³ = 150³

3a²b = 3 × 150² × 2

3ab² = 3 × 150 × 2²

b³ = 2³

Step 4: Add all the terms together:

(a + b)³ = a³ + 3a²b + 3ab² + b³

(150 + 2)³ = 150³ + 3 × 150² × 2 + 3 × 150 × 2² + 2³

152³ = 3,375,000 + 135,000 + 1,800 + 8

152³ = 3,511,808

Step 5: Hence, the cube of 152 is 3,511,808.

Using a Calculator

To find the cube of 152 using a calculator, input the number 152 and use the cube function (if available) or multiply 152 × 152 × 152. This operation calculates the value of 152³, resulting in 3,511,808. It’s a quick way to determine the cube without manual computation.

Step 1: Ensure the calculator is functioning properly.

Step 2: Input 152

Step 3: If the calculator has a cube function, press it to calculate 152³.

Step 4: If there is no cube function on the calculator, simply multiply 152 three times manually.

Step 5: The calculator will display 3,511,808.

Tips and Tricks for the Cube of 152

  • The product of two or more perfect cube numbers is always a perfect cube.
  • A perfect cube can always be expressed as the product of three identical groups of equal prime factors.

Common Mistakes to Avoid When Calculating the Cube of 152

There are some typical errors that students might make during the process of cubing a number. Here are five major mistakes that students might make:

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Problem 1

What is the cube and cube root of 152?

Okay, lets begin

The cube of 152 is 3,511,808 and the cube root of 152 is approximately 5.331.

Explanation

First, let’s find the cube of 152.

We know that the cube of a number is such that x³ = y Where x is the given number, and y is the cubed value of that number

So, we get 152³ = 3,511,808

Next, we must find the cube root of 152 We know that the cube root of a number ‘x’ is such that ∛x = y Where ‘x’ is the given number, and y is the cube root value of the number

So, we get ∛152 ≈ 5.331

Hence, the cube of 152 is 3,511,808 and the cube root of 152 is approximately 5.331.

Well explained 👍

Problem 2

If the side length of the cube is 152 cm, what is the volume?

Okay, lets begin

The volume is 3,511,808 cm³.

Explanation

Use the volume formula for a cube V = Side³.

Substitute 152 for the side length: V = 152³ = 3,511,808 cm³.

Well explained 👍

Problem 3

How much larger is 152³ than 142³?

Okay, lets begin

152³ – 142³ = 992,560.

Explanation

First, find the cube of 152, which is 3,511,808

Next, find the cube of 142, which is 2,519,248

Now, find the difference between them using the subtraction method. 3,511,808 – 2,519,248 = 992,560

Therefore, 152³ is 992,560 larger than 142³.

Well explained 👍

Problem 4

If a cube with a side length of 152 cm is compared to a cube with a side length of 12 cm, how much larger is the volume of the larger cube?

Okay, lets begin

The volume of the cube with a side length of 152 cm is 3,511,808 cm³.

Explanation

To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object).

Cubing 152 means multiplying 152 by itself three times: 152 × 152 = 23,104, and then 23,104 × 152 = 3,511,808.

The unit of volume is cubic centimeters (cm³) because we are calculating the space inside the cube.

Therefore, the volume of the cube is 3,511,808 cm³.

Well explained 👍

Problem 5

Estimate the cube 151.5 using the cube of 152.

Okay, lets begin

The cube of 151.5 is approximately 3,511,808.

Explanation

First, identify the cube of 152.

The cube of 152 is 152³ = 3,511,808.

Since 151.5 is only slightly less than 152, the cube of 151.5 will be almost the same as the cube of 152.

The cube of 151.5 is approximately 3,511,808

because the difference between 151.5 and 152 is very small.

So, we can approximate the value as 3,511,808.

Well explained 👍

FAQs on Cube of 152

1.What are the perfect cubes up to 152?

The perfect cubes up to 152 are 1, 8, 27, 64, and 125.

2.How do you calculate 152³?

To calculate 152³, use the multiplication method: 152 × 152 × 152, which equals 3,511,808.

3.What is the meaning of 152³?

152³ means 152 multiplied by itself three times, or 152 × 152 × 152.

4.What is the cube root of 152?

5.Is 152 a perfect cube?

No, 152 is not a perfect cube because no integer multiplied by itself three times equals 152.

Important Glossaries for Cube of 152

  • Binomial Formula: An algebraic expression used to expand the powers of a number, written as (a + b)ⁿ, where ‘n’ is a positive integer. The formula is used to find the square and cube of a number.
  • Cube of a Number: Multiplying a number by itself three times is called the cube of a number. 
  • Exponential Form: A way of expressing numbers using a base and an exponent (or power), where the exponent value indicates how many times the base is multiplied by itself. For example, 2³ represents 2 × 2 × 2, which equals 8. 
  • Perfect Cube: A number that can be expressed as the cube of an integer. 
  • Cube Root: A number that, when multiplied by itself three times, gives the original number.

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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.