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 8000, and its examples.
The cube root of 8000 is the value which, when multiplied by itself three times (cubed), gives the original number 8000. The cube root of 8000 is 20. The cube root of 8000 is expressed as ∛8000 in radical form, where the “ ∛ ” sign” is called the “radical” sign. In exponential form, it is written as (8000)⅓. If “m” is the cube root of 8000, then, m3=8000. Let us find the value of “m”.
The cube root of 8000 can be found through various methods like:
The steps involved to find ∛8000 are:
Step 1: Find the prime factors of 8000
After factoring 8000, make groups of three same factors out of the prime factors to get the cube root.
8000 = 2×2×2×2×2×2×5×5×5
∛8000 = ∛(2×2×2×2×2×2×5×5×5)= 2×2×5=20
After grouping together three same factors at a time, put the remaining factor under ∛.
Here, for 8000, no remaining factors are there. We get 3 groups of prime factor, i.e., (2×2×2), (2×2×2), (5×5×5)
So, 8000 is a Perfect cube. ∛8000=20.
Understanding common misconceptions or mistakes can make your calculations error free. So let us see how to avoid those from happening.
Find ((∛8000/ ∛1331) × (∛8000/ ∛1728))
((∛8000/ ∛1331) × (∛8000/ ∛1728))
=(20/ 11)× (20 / 12)
=400/132
Answer: 400/132
Simplified the expression and found the answer.
The length, breadth, and height of a cuboid is 10 units, 4 units, and 5 cm respectively. To find its volume, also find the measure of a side of a cube, whose volume is 8000 cubic units.
Volume of a cuboid = length × breadth × height = 10 × 4 × 5 cubic units = 200 cubic units.
Given, Volume of a cube = 8000 cubic units
⇒ side × side × side = 8000 cubic units
⇒ side = ∛8000
⇒ side = 20 units
Answer: Volume of the cuboid = 200 cubic units
Side length of the cube = 20 units
Applied the formula and concept of the volume of a cuboid and cube and solved.
Multiply ∛8000 / ∛216
∛8000/∛216
= 20/6
= 10/3
Answer: 10/3
We know that the cubic root of 216 is 6, hence dividing ∛8000 by ∛216.
What is ∛(8000⁶×¹/⁶) ?
∛(80006×1/6)
= (8000)1/3
= 20
Answer: 20
We solved and simplified the exponent part first using the fact that, (80006×1/6)=20, then solved.
Find ∛(7000-(-1000)).
∛(7000-(-1000))
= ∛(7000+1000)
=∛8000
=20
Answer: 20
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.