Cube Root of 49
2026-02-21 20:55 Diff
https://brightchamps.com/en-us/math/algebra/cube-root-of-49

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Last updated on August 5, 2025

The cube root of 49 is the value that, when multiplied by itself three times (cubed), gives the original number 49. Do you know? Cube roots apply to our real life also, like that for measuring dimensions, creating digital art, field of engineering, making financial decisions etc.

What Is the Cube Root of 49?

The cube root of 49 is 3.65930571002. The cube root of 49 is expressed as ∛49 in radical form, where the “ ∛ ”  sign" is called the “radical” sign. In exponential form, it is written as (49)⅓. If “m” is the cube root of 49, then, m3=49. Let us find the value of “m”.

Finding the Cubic Root of 49

We can find cube root of 49 through a method, named as, Halley’s Method. Let us see how it finds the result.
 

Cubic Root of 49 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 49.


Step 1: Let a=49. Let us take x as 3, since, 33=27 is the nearest perfect cube which is less than 49.


Step 2: Apply the formula.  ∛49≅ 3((33+2×49) / (2(3)3+49))= 3.64…


Hence, 3.64… is the approximate cubic root of 49.
 

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Common Mistakes and How to Avoid Them in the Cube Root of 49

Understanding common misconceptions or mistakes can make your calculations error free. So let us see how to avoid those from happening.

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Problem 1

Find ((∛98/ ∛49) × (∛98/ ∛49) × (∛98/ ∛49))

Okay, lets begin

 (∛98/ ∛49) × (∛98/ ∛49) × (∛98/ ∛49)


= (∛98× ∛98× ∛98) / (∛49× ∛49× ∛49)


=((98)⅓)3/ ((49)⅓)3


=98/49


=2


Answer: 2
 

Explanation

 We solved and simplified the exponent part first using the fact that, ∛98=(98)⅓ and ∛49=(49)⅓ , then solved.
 

Well explained 👍

Problem 2

If y = ∛49, find y³/ y⁶

Okay, lets begin

 y=∛49


⇒ y3/y6= (∛49)3 / (∛49)6


⇒ y3/y6= 49/ (49)2= 1/49


Answer: 1/49
 

Explanation

(∛49)3=(491/3)3

=49, and ∛(49)6

=(491/3)6=(49)2.

Using this, we found the value of y3/y6.
 

Well explained 👍

Problem 3

Multiply ∛49 × ∛64 × ∛125

Okay, lets begin

 ∛49 ×  ∛64  × ∛125

= 3.659 × 4 ×5

= 73.18


Answer:  73.18
 

Explanation

We know that the cubic root of 64 is 4 and the cubic root of 125 is 5, hence multiplying  ∛125, ∛64 and ∛49.
 

Well explained 👍

Problem 4

What is ∛(100)⁶+ ∛(49)⁶ ?

Okay, lets begin

 ∛(1006)+ ∛(49)6  

= ((100)6))1/3 +((49)6)1/3

=(100)2 + (49)2

= 10000 + 2401


Answer: 12401
 

Explanation

We solved and simplified the exponent part first using the fact that, ∛100=(100)⅓ and ∛49=(49)⅓ , then solved.
 

Well explained 👍

Problem 5

Find ∛(49+(-9)+(-13))

Okay, lets begin

 ∛(49-9-13)

= ∛27

=3


Answer: 3
 

Explanation

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

Well explained 👍

FAQs on 49 Cubic Root

1.What is a cube of 49?

The answer to the cube of 49 is 117649.
 

2.What is a square root of 49?

3.What is √48 simplified ?

√48 =√(3 ×2×2×2×2) = 4√3.
 

4.How to simplify the cube root of 48?

48 is a non-perfect cube, hence you can use the prime factorization method and Halley’s method to simplify it. 
 

5.Is 49 a real number?

Important Glossaries for Cubic Root of 49

  • Irrational Numbers - Numbers which cannot be expressed as p/q, where p and q are integers and q not equal to 0 are called Irrational numbers.
  • 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.
  • Approximation - Finding out a value which is nearly correct, but not perfectly correct.
  • 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.