Cube Root of 7
2026-02-28 11:23 Diff
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Last updated on August 5, 2025

The cube root of 7 is the value that, when multiplied by itself three times (cubed), gives the original number 7. Do you know? Cube roots apply to our real life also, like that for measuring volume and scaling, density and mass calculation, etc.

What Is the Cube Root of 7 ?

The cube root of 7 is 1.91293118277. The cube root of 7 is expressed as ∛7 in radical form, where the “∛"  sign is called the “radical” sign. In exponential form, it is written as (7)⅓. If “m” is the cube root of 7, then, m3=7.  Let us find the value of “m”.
 

Finding the Cube Root of 7

The Prime Factorization of 7 is 7, so, the cube root of 7 is expressed as ∛7 as its simplest radical form. We can find cube root of 7 through another method, named as, Halley’s Method. Let us see how it finds the result.
 

Cube Root of 7 By Halley’s Method

Now, what is Halley’s Method? It is an iterative method for finding cube roots of a given number N, such that, x3=N, where this method approximates the value of “x”.


Formula is ∛a≅ x((x3+2a) / (2x3+a)), where 


a=given number whose cube root you are going to find


x=integer guess for the cubic root


 Let us apply Halley’s method on the given number 7.


Step 1: Let a=7. Let us take x as 1, since, 1 is the nearest perfect cube which is less than 7.


Step 2: Apply the formula.  ∛7≅ 1((13+2×7) / (2(1)3+7))=15/9 ≅ 1.667


Hence, 1.667 is the approximate cubic root of 7.
 

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Common Mistakes and How to Avoid Them in the Cube Root of 7

some common mistakes and their solutions are given below:

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Problem 1

Find ∛7 / ∛8

Okay, lets begin

∛7/ ∛8= 1.913 / 2 =0.9565


Answer:     0.9565
 

Explanation

We know that the cubic root of 8 is 2, hence dividing  ∛7 by 2.

Well explained 👍

Problem 2

The Volume of a cube is 7 cubic centimeters, find the length of one side of the cube.

Okay, lets begin

We know that, (side of a cube)3=Volume of a cube


⇒side of the cube =  ∛(Volume of the cube)


⇒side of the cube = ∛7


⇒ side of the cube = 1.913 cm


Answer:     1.913 cm
 

Explanation

We applied the formula for finding the volume of a cube, and inverted it to find the measure of one side of the cube.
 

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Problem 3

Subtract ∛7 - ∛8

Okay, lets begin

 ∛7-∛8= 1.913–2= -0.087

Answer:        -0.913
 

Explanation

We know that the cubic root of 8 is 2, hence subtracting  ∛8 from ∛7.
 

Well explained 👍

Problem 4

What is ∛(7² ) ?

Okay, lets begin

 ∛(72) = ∛49 = 3.659… 


Answer:       3.659… 
 

Explanation

We first found the square value of 7, which is 49, and then found out the cube root of 49.
 

Well explained 👍

Problem 5

Find ∛(7+1).

Okay, lets begin

 ∛(7+1) = ∛8=2

Answer:        2
 

Explanation

Simplified the expression, and found out the cubic root of the result. 
 

Well explained 👍

FAQs on 7 Cube Root

1.How to calculate √7?

√7 can be calculated through various methods like Long Division method, Prime factorization method or, Estimation method. The value of √7 is 2.645… .
 

2.What is ∛7 in fraction?

Cube roots can be expressed in fractional form if and only if the original number is a fraction or, in certain cases, the cube root value is a rational number. Here, ∛7 = 1.913… is an irrational number, so it cannot be expressed as a fraction.
 

3.Is ∛7 real?

4.What is the order of ∛7?

The order of ∛7 is 3, because the order of a root refers to the degree of the root.
 

5.Is √7 a polynomial?

√7 is not a polynomial, since it is a constant number, and not a variable. It does not involve any variables raised to whole number exponents.

Important Glossaries for Cube Root of 7

  • Integers: Integers can be a positive natural number, negative of a positive number, or zero. We can perform all the arithmetic operations on integers. The examples of integers are, 1, 2, 5,8, -8, -12, etc.
  • Whole numbers:The whole numbers are part of the number system, which includes all the positive integers from 0 to infinity. 
  • Square root:The square root of a number is a value “y” such that when “y” is multiplied by itself → y × y, the result is the original number.
  • Polynomial: It is an algebraic expression made up of variables like “x” and constants, combined using addition, subtraction, multiplication, or division, where the variables are raised to whole number exponents.
  • Iterative method: This method is a mathematical process which uses an initial value to generate further and step-by-step sequence of solutions for a problem.

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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.