Last updated on May 26th, 2025
We will learn the cube root concept to use it on other mathematical topics like algebra, mensuration, geometry, trigonometry, etc. So, it is as important as learning square roots. Let us now see how we can obtain the cube root value of 1200, and its examples.
The cube root of 1200 is the value which, when multiplied by itself three times (cubed), gives the original number 1200. The cube root of 1200 is 10.6265856918. The cube root of 1200 is expressed as β1200 in radical form, where the “ β ” sign” is called the “radical” sign. In exponential form, it is written as (1200)β
. If “m” is the cube root of 1200, then, m3=1200. Let us find the value of “m”.
We can find cube roots of 1200 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 1200.
Step 1: Let a=1200. Let us take x as 10, since 103=1000 is the nearest perfect cube which is less than 1200.
Step 2: Apply the formula. β1200≅ 10((103+2×1200) / (2(10)3+1200)) = 10.62…
Hence, 10.62… is the approximate cubic root of 1200.
Understanding common misconceptions or mistakes can make your calculations error free. So let us see how to avoid those from happening.
Find β1200/ β600
β1200/ β600
= β(1200/600)
= β2
=1.2599…
Answer: 1.2599…
We found that the cubic root of 2 is 1.2599…, upon dividing β1200 by β600.
The volume of a cube is 1200 cubic centimeters, find the length of one side of the cube.
We know that, (side of a cube)3=Volume of a cube
⇒side of the cube = β(Volume of the cube)
⇒side of the cube = β1200
⇒ side of the cube = 10.62 cm
Answer: 10.62 cm
We applied the formula for finding the volume of a cube, and inverted it to find the measure of one side of the cube.
Subtract β1200 - β216, β1331-β1200
: β1200-β216
= 10.62–6
= 4.62
β1331-β1200
= 11–10.62 = 0.38
Answer: 4.62, 0.38
We know that the cubic root of 216 is 6, hence subtracting β216 from β1200. Applying the same for the next one, we know that the cubic root of 1331 is 11, hence subtracting β1200 from β1331.
What is β(1200Β²) ?
: β(12002) = (1200)2/3
Answer: (1200)2/3
Converting the given expression to exponential form.
Find β((1200+528)Γ(1200+997)).
β((1728)×(2197))
= β(1728×2197)
=β((12)3 × (13)3)
=β123 × β133
= 12 × 13
=156
Answer: 156
Simplified the expression, and found out the cubic root of the result.
2) The cube root of a negative number is also negative.
3) If the cube root of a number is a whole number, then that original number is said to be perfect cube
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.