256 LearnersLast updated on May 26th, 2025
Cube Root of 49
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 β49 in radical form, where the “ β ” sign" is called the “radical” sign. In exponential form, it is written as (49)β . 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 Halleyβs 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 βa≅ 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. β49≅ 3((33+2×49) / (2(3)3+49))= 3.64…
Hence, 3.64… is the approximate cubic root of 49.
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 β49, students can make error in the crucial part and may write as β49=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 β(49)³, students might do as β(49×3)
Clear the concepts again and again if they don’t understand where to do what. β(49)3≠β(49×3).
β(49)3= 49
Cube Root of 49 Examples
Problem 1
Find ((β98/ β49) Γ (β98/ β49) Γ (β98/ β49))
(β98/ β49) × (β98/ β49) × (β98/ β49)
= (β98× β98× β98) / (β49× β49× β49)
=((98)β
)3/ ((49)β
)3
=98/49
=2
Answer: 2
Explanation
We solved and simplified the exponent part first using the fact that, β98=(98)β
and β49=(49)β
, then solved.
Problem 2
If y = β49, find yΒ³/ yβΆ
y=β49
⇒ y3/y6= (β49)3 / (β49)6
⇒ y3/y6= 49/ (49)2= 1/49
Answer: 1/49
Explanation
(β49)3=(491/3)3
=49, and β(49)6
=(491/3)6=(49)2.
Using this, we found the value of y3/y6.
Problem 3
Multiply β49 Γ β64 Γ β125
β49 × β64 × β125
= 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 β125, β64 and β49.
Problem 4
What is β(100)βΆ+ β(49)βΆ ?
β(1006)+ β(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, β100=(100)β
and β49=(49)β
, then solved.
Problem 5
Find β(49+(-9)+(-13))
β(49-9-13)
= β27
=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 β48 simplified ?
4.How to simplify the cube root of 48?
5.Is 49 a real number?
6.How does learning Algebra help students in Saudi Arabia make better decisions in daily life?
7.How can cultural or local activities in Saudi Arabia support learning Algebra topics such as Cube Root of 49?
8.How do technology and digital tools in Saudi Arabia support learning Algebra and Cube Root of 49?
9.Does learning Algebra support future career opportunities for students in Saudi Arabia?
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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About BrightChamps in Saudi Arabia
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.
