Cube of 349
2026-02-28 21:42 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 when comparing sizes of objects or things with cubic measurements. In this topic, we shall learn about cubes of 349.

Cube of 349

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 349 can be written as 349³, which is the exponential form. Or it can also be written in arithmetic form as, 349 × 349 × 349.

How to Calculate the Value of Cube of 349

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. 349³ = 349 × 349 × 349 Step 2: You get 42,502,349 as the answer. Hence, the cube of 349 is 42,502,349.

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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 349 into two parts, as 300 and 49. Let a = 300 and b = 49, so a + b = 349 Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³ Step 3: Calculate each term a³ = 300³ 3a²b = 3 × 300² × 49 3ab² = 3 × 300 × 49² b³ = 49³ Step 4: Add all the terms together: (a + b)³ = a³ + 3a²b + 3ab² + b³ (300 + 49)³ = 300³ + 3 × 300² × 49 + 3 × 300 × 49² + 49³ 349³ = 27,000,000 + 13,230,000 + 2,158,500 + 117,649 349³ = 42,502,349 Step 5: Hence, the cube of 349 is 42,502,349.

Using a Calculator

To find the cube of 349 using a calculator, input the number 349 and use the cube function (if available) or multiply 349 × 349 × 349. This operation calculates the value of 349³, resulting in 42,502,349. 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 4 and 9 Step 3: If the calculator has a cube function, press it to calculate 349³. Step 4: If there is no cube function on the calculator, simply multiply 349 three times manually. Step 5: The calculator will display 42,502,349.

Tips and Tricks for the Cube of 349

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 349

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 349?

Okay, lets begin

The cube of 349 is 42,502,349 and the cube root of 349 is approximately 7.054.

Explanation

First, let’s find the cube of 349. We know that the 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 349³ = 42,502,349 Next, we must find the cube root of 349 We know that the cube root of a number ‘x’, such that ³√x = y Where ‘x’ is the given number, and y is the cube root value of the number So, we get ³√349 ≈ 7.054 Hence the cube of 349 is 42,502,349 and the cube root of 349 is approximately 7.054.

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Problem 2

If the side length of the cube is 349 cm, what is the volume?

Okay, lets begin

The volume is 42,502,349 cm³.

Explanation

Use the volume formula for a cube V = Side³. Substitute 349 for the side length: V = 349³ = 42,502,349 cm³.

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Problem 3

How much larger is 349³ than 300³?

Okay, lets begin

349³ – 300³ = 15,502,349.

Explanation

First, find the cube of 349, which is 42,502,349. Next, find the cube of 300, which is 27,000,000. Now, find the difference between them using the subtraction method. 42,502,349 – 27,000,000 = 15,502,349 Therefore, 349³ is 15,502,349 larger than 300³.

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Problem 4

If a cube with a side length of 349 cm is compared to a cube with a side length of 49 cm, how much larger is the volume of the larger cube?

Okay, lets begin

The volume of the cube with a side length of 349 cm is 42,502,349 cm³, which is much larger.

Explanation

To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object). Cubing 349 means multiplying 349 by itself three times: 349 × 349 = 121,801, and then 121,801 × 349 = 42,502,349. The unit of volume is cubic centimeters (cm³), because we are calculating the space inside the cube. Therefore, the volume of the cube is 42,502,349 cm³.

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Problem 5

Estimate the cube of 348 using the cube of 349.

Okay, lets begin

The cube of 348 is approximately 42,502,349.

Explanation

First, identify the cube of 349, The cube of 349 is 349³ = 42,502,349. Since 348 is only a tiny bit less than 349, the cube of 348 will be almost the same as the cube of 349. The cube of 348 is approximately 42,502,349 because the difference between 348 and 349 is very small. So, we can approximate the value as 42,502,349.

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FAQs on Cube of 349

1.What are the perfect cubes up to 349?

The perfect cubes up to 349 are 1, 8, 27, 64, 125, 216, and 343.

2.How do you calculate 349³?

To calculate 349³, use the multiplication method, 349 × 349 × 349, which equals 42,502,349.

3.What is the meaning of 349³?

349³ means 349 multiplied by itself three times, or 349 × 349 × 349.

4.What is the cube root of 349?

5.Is 349 a perfect cube?

No, 349 is not a perfect cube because no integer multiplied by itself three times equals 349.

Important Glossaries for Cube of 349

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 equal to 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 3³. Cube Root: The cube root of a number is a value 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.