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Last updated on November 30th, 2024
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 225, and its examples.
The cube root of 225 is the value which, when multiplied by itself three times (cubed), gives the original number 225. The cube root of 225 is 6.08220199557. The cube root of 225 is expressed as β225 in radical form, where the “ β ” sign” is called the “radical” sign. In exponential form, it is written as (225)β
. If “m” is the cube root of 225, then, m3=225. Let us find the value of “m”.
We can find cube roots of 225 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 225.
Step 1: Let a=225. Let us take x as 6, since 63=216 is the nearest perfect cube which is less than 216.
Step 2: Apply the formula. β216≅ 6((63+2×225) / (2(6)3+225)) = 6.08…
Hence, 6.08… is the approximate cubic root of 225.
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