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427 LearnersLast updated on August 5, 2025
Cube Root of 49
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.
Mistake 1
Students might make errors during factorization. For ∛49, students can make error in the crucial part and may write as ∛49=73
Prime Factorization is a crucial part in determining cube roots and square roots. So, use the exact prime factors and group (or pair)
Mistake 2
Students forget the concept of cube roots often, by not understanding the definition.
This happens because of uncleared understanding of cube roots and the methods to find it.
Mistake 3
For large non-perfect cubes, students often estimate wrongly and leave it with a wrong result.
Keep the methods of finding cube roots in front whenever attempting large non-perfect cubes.
Mistake 4
Students often depend on memorizing rather than understanding concepts of cube root.
Memorizing is not the solution when it comes to complex problems.It is advisable to get the proper understanding of the methods of finding cube roots.
Mistake 5
Misapply the cube root property like when asked to solve ∛(49)³, students might do as ∛(49×3)
Clear the concepts again and again if they don’t understand where to do what. ∛(49)3≠∛(49×3).
∛(49)3= 49
Cube Root of 49 Examples
Problem 1
Find ((∛98/ ∛49) × (∛98/ ∛49) × (∛98/ ∛49))
(∛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.
Problem 2
If y = ∛49, find y³/ y⁶
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.
Problem 3
Multiply ∛49 × ∛64 × ∛125
∛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.
Problem 4
What is ∛(100)⁶+ ∛(49)⁶ ?
∛(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.
Problem 5
Find ∛(49+(-9)+(-13))
∛(49-9-13)
= ∛27
=3
Answer: 3
Explanation
Simplified the expression, and found out the cubic root of the result.
FAQs on 49 Cubic Root
1.What is a cube of 49?
2.What is a square root of 49?
3.What is √48 simplified ?
4.How to simplify the cube root of 48?
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.
