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 625, and its examples.
The cube root of 625 is the value which, when multiplied by itself three times (cubed), gives the original number 625. The cube root of 625 is 8.54987973338. The cube root of 625 is expressed as ∛625 in radical form, where the “ ∛ ” sign” is called the “radical” sign. In exponential form, it is written as (625)â…“. If “m” is the cube root of 625, then, m3=625. Let us find the value of “m”.
We can find cube root of 625 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 625.
Step 1: Let a=625. Let us take x as 8, since 83=512 is the nearest perfect cube which is less than 625.
Step 2: Apply the formula. ∛625≅ 8((83+2×625) / (2(8)3+625))= 8.55…
Hence, 8.55… is the approximate cubic root of 625.
Understanding common misconceptions or mistakes can make your calculations error free. So let us see how to avoid those from happening.
Find ∛625/ ∛8
∛625/ ∛8
= 8.54/ 2
= 4.27
Answer: 4.27
We know that the cubic root of 8 is 2, hence dividing ∛625 by 2.
The volume of a cube is 625 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 = ∛(Volume of the cube)
⇒side of the cube = ∛625
⇒ side of the cube = 8.54 cm
Answer: 8.54 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 ∛625 - ∛8
∛625-∛8
= 8.54–2
= 6.54
Answer: 6.54
We know that the cubic root of 8 is 2, hence subtracting ∛8 from ∛625.
What is ∛(625²) ?
∛(6252)
= (625)2/3
Answer: (625)2/3
Converting it to the exponential form, the cube root of 625 means (625)1/3 , and then again squaring it.
Find ∛(625+104)
∛(625+104)
= ∛729
=9
Answer: 9
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.