Last updated on May 26th, 2025
The cube root of 10 is the value that, when multiplied by itself three times (cubed), gives the original number 10. Do you know? Cube roots apply to our real life also, like that for measuring dimensions, density and mass, field of engineering etc.
The cube root of 10 is 2.15443469003. The cube root of 10 is expressed as ∛10 in radical form, where the “ ∛ “ sign is called the “radical” sign. In exponential form, it is written as (10)1/3. If “m” is the cube root of 10, then, m3=10. Let us find the value of “m”.
The cube root of 10 is expressed as ∛10 as its simplest radical form. We can find cube root of 10 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 10.
Step 1: Let a=10. Let us take x as 2, since, 23=8 is the nearest perfect cube which is less than 10.
Step 2: Apply the formula. ∛10≅ 2((23+2×10) / (2(2)3+10))=2.15
Hence, 2.15 is the approximate cubic root of 10.
some common mistakes with their solutions are given below:
The length, breadth, and height of a cuboid is 2 units, 2.5 units, and 2.8 units respectively. To find its volume, also find the measure of a side of a cube whose volume is 10 cubic units.
Volume of a cuboid = length × breadth × height = 2 × 2.5 × 2.8 cubic units = 14 cubic units.
Given, Volume of a cube = 10 cubic units
⇒ side × side × side = 10 cubic units
⇒ side = ∛10
⇒ side = 2.154 units
Answer: Volume of the cuboid = 14 cubic units
Side length of the cube = 2.154 units
Applied the formula and concept of the volume of a cuboid and cube and solved.
If y = ∛10, find y³/ y⁶
y=∛10
⇒ y3/y6= (∛10)3 / (∛10)6
⇒ y3/y6= 10/ (10)2= 1/10
Answer: 1/10
(∛10)3=(101/3)3=10, and (∛10)6=(101/3)6=(10)2.
Using this, we found the value of y3/y6.
Multiply ∛10 × ∛27 × ∛64
∛10×∛27× ∛64
= 2.154×3×4
= 25.848.
Answer: 25.848
We know that the cubic root of 27 is 3 and that of 64 is 4, hence multiplying.
What is ∛(10⁶) ?
∛(106)
= ((10)6))1/3
=(10)2
= 100
Answer: 100
We solved and simplified the exponent part first using the fact that, ∛10=(10)⅓, then solved.
Find ∛10 / 21.54.
(∛10) / 21.54
= 2.154 /21.54
=0.1
Answer: 0.1
Simplified the expression, and found out 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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