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133 LearnersLast updated on November 30th, 2024
Cube Root of 12
The cube root of 12 is the value which, when multiplied by itself three times (cubed), gives the original number 12. Do you know? Cube roots apply to our real life also, like that for measuring dimensions, density and mass, field of engineering etc.
What Is the Cubic Root of 12?
The cube root of 12 is 2.28942848511. The cube root of 12 is expressed as ∛12 in radical form, where the “ ∛ “ sign is called the “radical” sign. In exponential form, it is written as (12)1/3. If “m” is the cube root of 12, then, m3=12. Let us find the value of “m”.
Finding the Cubic Root of 12
The cube root of 12 is expressed as ∛12 as its simplest radical form, since 12 = 2×2×3
∛12 = ∛(2×2×3)
Group together three same factors at a time and put the remaining factor under ∛.
∛12= ∛12
We can find cube root of 12 through a method, named Halley’s Method. Let us see how it finds the result.
Cubic Root of 12 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 12.
Step 1: Let a=12. Let us take x as 2, since, 23=8 is the nearest perfect cube which is less than 12.
Step 2: Apply the formula. ∛12≅ 2((23+2×12) / (2(2)3+12))= 2.285…
Hence, 2.285… is the approximate cubic root of 12.
Important Glossaries for Cubic Root of 12
- Integers - Numbers which are positive, negative, or zero, and with which we can perform all the arithmetic operations, like addition, subtraction, multiplication and division, on integers. All integers are rational numbers. Ex: 1, 2, 5,6,8, -9, -12,-15 etc.
- Whole numbers - The whole numbers are part of the number system, which includes all the positive integers from 0 to infinity. These cannot be in fractional or decimal form.
- Square root -The square root of a number is a value, which, on multiplication by itself, gives the original number, such that √x = y, where y×y = x.
- 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, as if the approximate value is just near and close the original value.