Cube of 371
2026-02-28 10:05 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 used while comparing sizes of objects or things with cubic measurements. In this topic, we shall learn about the cube of 371.

Cube of 371

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 by itself three times results in a negative number.

The cube of 371 can be written as 371³, which is the exponential form.

Or it can also be written in arithmetic form as 371 × 371 × 371.

How to Calculate the Value of Cube of 371

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

  • By Multiplication Method
     
  • Using a Formula
     
  • Using a Calculator

By Multiplication Method

The multiplication method is a process in mathematics used to find the product of two 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. 371³ = 371 × 371 × 371

Step 2: You get 51,236,611 as the answer. Hence, the cube of 371 is 51,236,611.

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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 371 into two parts, as 300 and 71. Let a = 300 and b = 71, so a + b = 371

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

Step 3: Calculate each term \(a³ = 300³\) \(3a²b = 3 × 300² × 71\) \(3ab² = 3 × 300 × 71²\) \(b³ = 71³\)

Step 4: Add all the terms together: \((a + b)³ = a³ + 3a²b + 3ab² + b³\) \((300 + 71)³ = 300³ + 3 × 300² × 71 + 3 × 300 × 71² + 71³\) \(371³ = 27,000,000 + 19,170,000 + 4,533,000 + 357,911\) \(371³ = 51,236,611\)

Step 5: Hence, the cube of 371 is 51,236,611.

Using a Calculator

To find the cube of 371 using a calculator, input the number 371 and use the cube function (if available) or multiply 371 × 371 × 371. This operation calculates the value of 371³, resulting in 51,236,611. It’s a quick way to determine the cube without manual computation.

Step 1: Ensure the calculator is functioning properly.

Step 2: Press 3 followed by 7 and 1

Step 3: If the calculator has a cube function, press it to calculate 371³.

Step 4: If there is no cube function on the calculator, simply multiply 371 three times manually.

Step 5: The calculator will display 51,236,611.

Tips and Tricks for the Cube of 371

  • The cube of any even number is always even, while the cube of any odd number is always odd.
     
  • 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 371

There are some typical errors that kids might make during the process of cubing a number. Let us take a look at five of the major mistakes that kids might make:

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Problem 1

What is the cube and cube root of 371?

Okay, lets begin

The cube of 371 is 51,236,611 and the cube root of 371 is approximately 7.165.

Explanation

First, let’s find the cube of 371.

We know that cube of a number, such that x³ = y

Where x is the given number, and y is the cubed value of that number

So, we get 371³ = 51,236,611 Next, we must find the cube root of 371

We know that the cube root of a number ‘x’, such that ∛x = y

Where ‘x’ is the given number, and y is the cube root value of the number

So, we get ∛371 ≈ 7.165

Hence, the cube of 371 is 51,236,611 and the cube root of 371 is approximately 7.165.

Well explained 👍

Problem 2

If the side length of the cube is 371 cm, what is the volume?

Okay, lets begin

The volume is 51,236,611 cm³.

Explanation

Use the volume formula for a cube V = Side³.

Substitute 371 for the side length: V = 371³ = 51,236,611 cm³.

Well explained 👍

Problem 3

How much larger is 371³ than 300³?

Okay, lets begin

371³ – 300³ = 24,236,611.

Explanation

First find the cube of 371³, that is 51,236,611

Next, find the cube of 300³, which is 27,000,000

Now, find the difference between them using the subtraction method. 51,236,611 – 27,000,000 = 24,236,611

Therefore, 371³ is 24,236,611 larger than 300³.

Well explained 👍

Problem 4

If a cube with a side length of 371 cm is compared to a cube with a side length of 71 cm, how much larger is the volume of the larger cube?

Okay, lets begin

The volume of the cube with a side length of 371 cm is 51,236,611 cm³.

Explanation

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

Cubing 371 means multiplying 371 by itself three times: 371 × 371 = 137,641, and then 137,641 × 371 = 51,236,611.

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

Therefore, the volume of the cube is 51,236,611 cm³.

Well explained 👍

Problem 5

Estimate the cube 370 using the cube 371.

Okay, lets begin

The cube of 370 is approximately 50,653,000.

Explanation

First, identify the cube of 371,

The cube of 371 is 371³ = 51,236,611.

Since 370 is only slightly less than 371, the cube of 370 will be slightly less than the cube of 371.

The cube of 370 is approximately 50,653,000 because the difference between 370 and 371 is minimal.

So, we can approximate the value as 50,653,000.

Well explained 👍

FAQs on Cube of 371

1.What are the perfect cubes up to 371?

The perfect cubes up to 371 are 1, 8, 27, 64, 125, 216, and 343.

2.How do you calculate 371³?

To calculate 371³, use the multiplication method, 371 × 371 × 371, which equals 51,236,611.

3.What is the meaning of 371³?

371³ means 371 multiplied by itself three times, or 371 × 371 × 371.

4.What is the cube root of 371?

5.Is 371 a perfect cube?

No, 371 is not a perfect cube because no integer multiplied by itself three times equals 371.

Important Glossaries for Cube of 371

  • Binomial Formula: It is an algebraic expression used to expand the powers of a number, written as \((a + b)^n\), where ‘n’ is a positive integer raised to the base. 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: It is 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. For example, 27 is a perfect cube because it is 3 × 3 × 3.
     
  • Cube Root: A number that must be multiplied by itself three times to equal a given number. For example, the cube root of 27 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.