Table Of Contents
172 LearnersLast updated on February 13th, 2025
Cube Root of 4096
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 4096, and its examples.
What Is the Cube Root of 4096?
The cube root of 4096 is the value which, when multiplied by itself three times (cubed), gives the original number 4096. The cube root of 4096 is 16. The cube root of 4096 is expressed as ∛4096 in radical form, where the “ ∛ ” sign” is called the “radical” sign. In exponential form, it is written as (4096)⅓. If “m” is the cube root of 4096, then, m3=4096. Let us find the value of “m”.
Finding the Cubic Root of 4096
The cube root of 4096 can be found through various methods like:
- Prime Factorization method
- Subtraction method
Cube Root of 4096 by Prime Factorization method
The steps involved to find ∛4096 are:
Find the prime factors of 4096
After factoring 4096, make groups of three same factors out of the prime factors to get the cube root.
4096 = 2×2×2×2×2×2×2×2×2×2×2×2
∛4096 = ∛(2×2×2×2×2×2×2×2×2×2×2×2)= 2×2×2×2=16
After grouping together three same factors at a time, put the remaining factor under ∛.
Here, for 4096, no remaining factors are there. We get 4 groups of prime factor 2, i.e., (2×2×2), (2×2×2), (2×2×2), (2×2×2)
So, 4096 is a Perfect cube. ∛4096=16.
Common Mistakes and How to Avoid Them in the Cube Root of 4096
Understanding common misconceptions or mistakes can make your calculations error free. So let us see how to avoid those from happening.
Mistake 1
For ∛4096, students can make error in the important part of prime factorization
Prime Factorization is a crucial part in determining cube roots and square roots. So, use the exact prime factors and group (or pair).
Cube Root of 4096 Examples
Problem 1
Solve the equation: (x)³/²=4096
:(x)3/2=4096
⇒ (x)1/2=(4096)1/3
⇒ (x)1/2 = 16
⇒ (x) = (16)2
⇒ x= 256
Answer: 256
Explanation
Simplified the equation applying the cube root features and found the answer.
Problem 2
The length, breadth, and height of a cuboid is 10 units, 40 units, and 5 cm respectively. To find its volume, also find the measure of a side of a cube, whose volume is 4096 cubic units.
Volume of a cuboid = length × breadth × height = 10 × 40 × 5 cubic units = 2000 cubic units.
Given, Volume of a cube = 4096 cubic units
⇒ side × side × side = 4096 cubic units
⇒ side = ∛4096
⇒ side = 16 units
Answer: Volume of the cuboid = 2000 cubic units
Side length of the cube = 16 units
Explanation
Applied the formula and concept of the volume of a cuboid and cube and solved.
Problem 3
)Multiply ∛8000 / ∛216
∛8000/∛216
= 20/6
= 10/3
Answer: 10/3
Explanation
We know that the cubic root of 216 is 6, hence dividing ∛8000 by ∛216.
Problem 4
What is ∛(8000⁶*¹/⁶) ?
∛(80006×1/6)
= (8000)1/3
= 20
Answer: 20
Explanation
We solved and simplified the exponent part first using the fact that, (80006×1/6)=20, then solved.
Problem 5
If ∛4096 = a, find a³+ (1/a³)
a=∛4096=16
So, a3=163 and 1/a3=1/163
a3+ (1/a3)= 163 + 1/163 =4096 + (1/4096)
Answer: 4096 + (1/4096)
Explanation
found the cube root of 4096 and again converted to its cube according to the given expression.
FAQs on 4096 Cube Root
1.How do you find the cube root of 4096?
2.How to solve ∛4913 ?
3.Is 12167 a perfect cube?
4.Why is 200 not a perfect cube?
5.Is 32768 a perfect cube?
Important Glossaries for Cube Root of 4096
- Cube root properties - The features when cube root is applied to any number. Those are: 1) The cube root of all odd numbers is an odd number. The same applies for even numbers also, that is, the cube of any even number is even.
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
- Irrational Numbers - Numbers which cannot be expressed as m/n form, where m and n are integers and n not equal to 0, are called Irrational numbers.
- Square root -The square root of a number is a number which when multiplied by itself produces the original number, whose square root is to be found out.
- Polynomial - It is an algebraic expression made up of variables like “x” and constants, combined using addition, subtraction, multiplication, or division, where the variables are raised to whole number exponents.
Explore More algebra
Previous to Cube Root of 4096
Jaskaran Singh Saluja
About the Author
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.
Fun Fact
: He loves to play the quiz with kids through algebra to make kids love it.
