Last updated on May 26th, 2025
The cube root of 121 is the value that, when multiplied by itself three times (cubed), gives the original number 121. Do you know? Cube roots apply to our real life also, like that for measuring dimensions, designing structures, density and mass, field of engineering etc.
The cube root of 121 is 4.94608744325. The cube root of 121 is expressed as ∛121 in radical form, where the “ ∛ “ sign” is called the “radical” sign. In exponential form, it is written as (121)1/3. If “m” is the cube root of 121, then, m3=121. Let us find the value of “m”.
We can find cube root of 121 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 ∛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 121.
Step 1: Let a=121. Let us take x as 4, since 43=64 is the nearest perfect cube which is less than 121.
Step 2: Apply the formula. ∛121≅ 4((43+2×121) / (2(4)3+121))= 4.92
Hence, 4.92 is the approximate cubic root of 121.
some common mistakes with their solutions are given :
Find (∛120/ ∛121) × (∛123/ ∛121) × (∛122/ ∛121)
(∛120/ ∛121) × (∛123/ ∛121) × (∛122/ ∛121)
= (∛120× ∛123× ∛122) / (∛121× ∛121× ∛121)
=(∛120× ∛123× ∛122)/ ((121)⅓)3
=(∛120× ∛123× ∛122)/121
=(4.932 × 4.973 × 4.959)/ 121
Answer: (4.932 × 4.973 × 4.959)/ 121
We used the fact that ((121)⅓)3=121 and then found the cube roots of 120,122, and 123 and simplified.
The length, breadth, and height of a cuboid is 6 units, 6.5 units, and 4.5 cm respectively. To find its volume, also find the measure of a side of a cube, whose volume is 121 cubic units.
Volume of a cuboid = length × breadth × height = 6 × 6.5 × 4.5 cubic units = 175.5 cubic units.
Given, Volume of a cube = 121 cubic units
⇒ side × side × side = 121 cubic units
⇒ side = ∛121
⇒ side = 4.94 units
Answer: Volume of the cuboid = 175.5 cubic units
Side length of the cube = 4.94 units
Applied the formula and concept of the volume of a cuboid and cube and solved.
Multiply ∛121 × ∛125
∛121×∛125
= 4.94×5
= 24.7
Answer: 37.44
We know that the cubic root of 125 is 5, hence multiplying ∛125 with ∛121.
What is ∛(121⁶*¹/⁶) ?
∛(1216×1/6)
= (121)1/3
= 4.94…
Answer: 4.94
We solved and simplified the exponent part first using the fact that, (1216×1/6)=121, then solved.
Find ∛(121-(-4)).
∛(121-(-4))
= ∛(121+4)
=∛125=5
Answer: 5
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.
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