Cube Root of 749
2026-02-28 09:49 Diff
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Last updated on August 5, 2025

A number that, when multiplied by itself three times, gives the original number is its cube root. It has various applications in real life, such as determining the dimensions of cube-shaped objects and designing structures. We will now explore the cube root of 749 and explain the methods used to find it.

What is the Cube Root of 749?

We have learned the definition of the cube root. Now, let’s learn how it is represented using a symbol and exponent. The symbol we use to express the cube root is the radical sign (∛), and the exponent we use is ⅓.

In exponential form, ∛749 is written as 749(1/3). The cube root is just the opposite operation of finding the cube of a number. For example: Assume ‘y’ as the cube root of 749, then y3 can be 749. Since the cube root of 749 is not an exact value, we can write it as approximately 9.0802.

Finding the Cube Root of 749

Finding the cube root of a number involves identifying the number that must be multiplied three times to result in the target number. Now, we will go through the different ways to find the cube root of 749. The common methods we follow to find the cube root are given below:

  • Prime factorization method
  • Approximation method
  • Subtraction method
  • Halley’s method

To find the cube root of a non-perfect number like 749, we often follow Halley’s method.

Cube Root of 749 by Halley’s Method

Let's find the cube root of 749 using Halley’s method.

The formula is: ∛a ≅ x((x3 + 2a) / (2x3 + a))

where: a = the number for which the cube root is being calculated

x = the nearest perfect cube

Substituting,

a = 749;

x = 9

∛a ≅ 9((93 + 2 × 749) / (2 × 93 + 749))

∛749 ≅ 9((729 + 2 × 749) / (2 × 729 + 749))

∛749 ≅ 9.0802

The cube root of 749 is approximately 9.0802.

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Common Mistakes and How to Avoid Them in the Cube Root of 749

Finding the cube root of a number without any errors can be a challenging task. This happens for many reasons. Here are a few mistakes commonly made and ways to avoid them:

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Problem 1

Imagine you have a cube-shaped container that has a total volume of 749 cubic centimeters. Find the length of one side of the cube equal to its cube root.

Okay, lets begin

Side of the cube = ∛749 ≈ 9.08 units

Explanation

To find the side of the cube, we need to find the cube root of the given volume.

Therefore, the side length of the cube is approximately 9.08 units.

Well explained 👍

Problem 2

A company manufactures 749 cubic meters of material. Calculate the amount of material left after using 300 cubic meters.

Okay, lets begin

The amount of material left is 449 cubic meters.

Explanation

To find the remaining material, we need to subtract the used material from the total amount:

749 - 300 = 449 cubic meters.

Well explained 👍

Problem 3

A bottle holds 749 cubic meters of volume. Another bottle holds a volume of 150 cubic meters. What would be the total volume if the bottles are combined?

Okay, lets begin

The total volume of the combined bottles is 899 cubic meters.

Explanation

Let’s add the volume of both bottles:

749 + 150 = 899 cubic meters.

Well explained 👍

Problem 4

When the cube root of 749 is multiplied by 2, calculate the resultant value. How will this affect the cube of the new value?

Okay, lets begin

2 × 9.08 ≈ 18.16 The cube of 18.16 ≈ 5980.2

Explanation

When we multiply the cube root of 749 by 2, it results in a significant increase in the volume because the cube increases exponentially.

Well explained 👍

Problem 5

Find ∛(375 + 374).

Okay, lets begin

∛(375 + 374) = ∛749 ≈ 9.08

Explanation

As shown in the question ∛(375 + 374), we can simplify that by adding them.

So, 375 + 374 = 749.

Then we use this step: ∛749 ≈ 9.08 to get the answer.

Well explained 👍

FAQs on 749 Cube Root

1.Can we find the Cube Root of 749?

No, we cannot find the cube root of 749 exactly as the cube root of 749 is not a whole number. It is approximately 9.0802.

2.Why is Cube Root of 749 irrational?

The cube root of 749 is irrational because its decimal value goes on without an end and does not repeat.

3.Is it possible to get the cube root of 749 as an exact number?

No, the cube root of 749 is not an exact number. It is a decimal that is about 9.0802.

4.Can we find the cube root of any number using prime factorization?

Prime factorization can be used to calculate the cube root of perfect cube numbers, but it is not the right method for non-perfect cube numbers. For example, 2 × 2 × 2 = 8, so 8 is a perfect cube.

5.Is there any formula to find the cube root of a number?

Yes, the formula we use for the cube root of any number ‘a’ is a^(1/3).

Important Glossaries for Cube Root of 749

  • Cube root: The number that, when multiplied three times by itself, yields the given number is the cube root of that number.
     
  • Perfect cube: A number is a perfect cube when it is the product of multiplying a number three times by itself. A perfect cube always results in a whole number. For example, 2 × 2 × 2 = 8, therefore, 8 is a perfect cube.
     
  • Exponent: The exponent form of the number denotes the number of times a number can be multiplied by itself. In a^(1/3), 1/3 is the exponent which denotes the cube root.
     
  • Radical sign: The symbol used to represent a root is expressed as (∛).
     
  • Irrational number: Numbers that cannot be expressed as a simple fraction are irrational. For example, the cube root of 749 is irrational because its decimal form goes on continuously without repeating.

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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.