Last updated on May 26th, 2025
The cube root of 25 is the value which, when multiplied by itself three times (cubed), gives the original number 25. Do you know? Cube roots apply to our real life also, like that for measuring dimensions, density and mass, creating unique digital art etc.
The cube root of 25 is 2.92401773821. The cube root of 25 is expressed as β25 in radical form, where the “ β “ sign is called the “radical” sign. In exponential form, it is written as (25)1/3. If “m” is the cube root of 25, then, m3=25. Let us find the value of “m”.
The Prime Factorization of 25 is 5×5, so, the cube root of 25 is expressed as β25 as its simplest radical form. We can find the cube root of 25 through a method, named 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 25.
Step 1: Let a=25. Let us take x as 2, since, 23=8 is the nearest perfect cube which is less than 25.
Step 2: Apply the formula. β25≅ 2((23+2×25) / (2(2)3+25))= 2.82…
Hence, 2.82… is the approximate cubic root of 25.
some common mistakes with their solutions are given below:
Find β25/ β14
β25/ β14
= 2.924 / 2.410
= 2924/2410
=1.213
Answer: 1.213
We found that the cubic root of 14 is 2.410…, hence dividing β25 by β14.
The Volume of a cube is 25 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 = β25
⇒ side of the cube = 2.924 cm
Answer: 2.924 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 β25 - β8, β27-β25
β25-β8
= 2.924–2
=0.924
β27-β25
= 3-2.924
= 0.076
Answer: 0.924, 0.076
We know that the cubic root of 8 is 2, hence subtracting β8 from β25. Applying the same for the next one, we know that the cubic root of 27 is 3, hence subtracting β25 from β27.
What is β(25Β²) ?
β(252)
= β625
= 8.549…
Answer: 8.549…
We first found the square value of 25, which is 625, and then found out the cube root of 625.
Find β((25+2)Γ(25+39)).
β((25+2)×(25+39))
= β(27×64)
=β1728
= 12
Answer: 12
Simplified the expression, and found out the cubic root of 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.
: He loves to play the quiz with kids through algebra to make kids love it.