Cube of 175
2026-02-28 13:47 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 175.

Cube of 175

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 because a negative number multiplied by itself three times results in a negative number.

The cube of 175 can be written as 175³, which is the exponential form, or it can also be written in arithmetic form as 175 × 175 × 175.

How to Calculate the Value of Cube of 175

In order to check whether a number is a cube number or not, we can use the following three methods: the 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.

  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 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. 175³ = 175 × 175 × 175

Step 2: You get 5,359,375 as the answer. Hence, the cube of 175 is 5,359,375.

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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 175 into two parts, as 150 and 25. Let a = 150 and b = 25, so a + b = 175

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

Step 3: Calculate each term a³ = 150³ 3a²b = 3 × 150² × 25 3ab² = 3 × 150 × 25² b³ = 25³

Step 4: Add all the terms together:

(a + b)³ = a³ + 3a²b + 3ab² + b³

(150 + 25)³ = 150³ + 3 × 150² × 25 + 3 × 150 × 25² + 25³

175³ = 3,375,000 + 1,687,500 + 281,250 + 15,625

175³ = 5,359,375

Step 5: Hence, the cube of 175 is 5,359,375.

Using a Calculator

To find the cube of 175 using a calculator, input the number 175 and use the cube function (if available) or multiply 175 × 175 × 175. This operation calculates the value of 175³, resulting in 5,359,375. It’s a quick way to determine the cube without manual computation.

Step 1: Ensure the calculator is functioning properly.

Step 2: Press 1 followed by 7 and 5

Step 3: If the calculator has a cube function, press it to calculate 175³.

Step 4: If there is no cube function on the calculator, simply multiply 175 three times manually.

Step 5: The calculator will display 5,359,375.

Tips and Tricks for the Cube of 175

  • 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 175

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 175?

Okay, lets begin

The cube of 175 is 5,359,375 and the cube root of 175 is approximately 5.584.

Explanation

First, let’s find the cube of 175.

We know that the cube of a number is x³ = y, where x is the given number, and y is the cubed value of that number. So, we get 175³ = 5,359,375.

Next, we must find the cube root of 175. We know that the cube root of a number x is ∛x = y, where x is the given number, and y is the cube root value of the number.

So, we get ∛175 ≈ 5.584.

Hence, the cube of 175 is 5,359,375 and the cube root of 175 is approximately 5.584.

Well explained 👍

Problem 2

If the side length of the cube is 175 cm, what is the volume?

Okay, lets begin

The volume is 5,359,375 cm³.

Explanation

Use the volume formula for a cube V = Side³.

Substitute 175 for the side length: V = 175³ = 5,359,375 cm³.

Well explained 👍

Problem 3

How much larger is 175³ than 150³?

Okay, lets begin

175³ – 150³ = 1,984,375.

Explanation

First, find the cube of 175³, which is 5,359,375.

Next, find the cube of 150³, which is 3,375,000.

Now, find the difference between them using the subtraction method.

5,359,375 – 3,375,000 = 1,984,375.

Therefore, 175³ is 1,984,375 larger than 150³.

Well explained 👍

Problem 4

If a cube with a side length of 175 cm is compared to a cube with a side length of 25 cm, how much larger is the volume of the larger cube?

Okay, lets begin

The volume of the cube with a side length of 175 cm is 5,359,375 cm³.

Explanation

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

Cubing 175 means multiplying 175 by itself three times:

175 × 175 = 30,625, and 30,625 × 175 = 5,359,375.

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

Therefore, the volume of the cube is 5,359,375 cm³.

Well explained 👍

Problem 5

Estimate the cube of 174.9 using the cube of 175.

Okay, lets begin

The cube of 174.9 is approximately 5,359,375.

Explanation

First, identify the cube of 175.

The cube of 175 is 175³ = 5,359,375.

Since 174.9 is only a tiny bit less than 175, the cube of 174.9 will be almost the same as the cube of 175.

The cube of 174.9 is approximately 5,359,375 because the difference between 174.9 and 175 is very small.

So, we can approximate the value as 5,359,375.

Well explained 👍

FAQs on Cube of 175

1.What are the perfect cubes up to 175?

The perfect cubes up to 175 are 1, 8, 27, 64, and 125.

2.How do you calculate 175³?

To calculate 175³, use the multiplication method: 175 × 175 × 175, which equals 5,359,375.

3.What is the meaning of 175³?

175³ means 175 multiplied by itself three times, or 175 × 175 × 175.

4.What is the cube root of 175?

5.Is 175 a perfect cube?

No, 175 is not a perfect cube because no integer multiplied by itself three times equals 175.

Important Glossaries for Cube of 175

  • 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.
  • Volume of a Cube: The amount of space inside a cube, calculated as Side³, where the side is the length of one edge of the cube.
  • Perfect Cube: A number that is the cube of an integer. For example, 8 is a perfect cube because it equals 2 × 2 × 2.

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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.