Last updated on May 26th, 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.
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”.
We can find cube root of 49 through a method, named as, Halley’s Method. Let us see how it finds the result.
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.
Understanding common misconceptions or mistakes can make your calculations error free. So let us see how to avoid those from happening.
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
We solved and simplified the exponent part first using the fact that, β98=(98)β
and β49=(49)β
, then solved.
If y = β49, find yΒ³/ yβΆ
y=β49
⇒ y3/y6= (β49)3 / (β49)6
⇒ y3/y6= 49/ (49)2= 1/49
Answer: 1/49
(β49)3=(491/3)3
=49, and β(49)6
=(491/3)6=(49)2.
Using this, we found the value of y3/y6.
Multiply β49 Γ β64 Γ β125
β49 × β64 × β125
= 3.659 × 4 ×5
= 73.18
Answer: 73.18
We know that the cubic root of 64 is 4 and the cubic root of 125 is 5, hence multiplying β125, β64 and β49.
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
We solved and simplified the exponent part first using the fact that, β100=(100)β
and β49=(49)β
, then solved.
Find β(49+(-9)+(-13))
β(49-9-13)
= β27
=3
Answer: 3
Simplified the expression, and found out the cubic root of the result.
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.
: He loves to play the quiz with kids through algebra to make kids love it.