344 LearnersLast updated on May 26th, 2025
Cube Root of 1024
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 1024, and its examples.
What Is the Cube Root of 1024?
The cube root of 1024 is the value which, when multiplied by itself three times (cubed), gives the original number 1024. The cube root of 1024 is 10.0793683992. The cube root of 1024 is expressed as β1024 in radical form, where the “ β ” sign” is called the “radical” sign. In exponential form, it is written as (1024)β
. If “m” is the cube root of 1024, then, m3=1024. Let us find the value of “m”.
Finding the Cubic Root of 1024
We can find cube roots of 1024 through a method, named as, Halley’s Method. Let us see how it finds the result
Cubic Root of 1024 By Halleyβs Method
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 1024.
Step 1: Let a=1024. Let us take x as 10, since 103=1000 is the nearest perfect cube which is less than 1024.
Step 2: Apply the formula. β1024≅ 10((103+2×1024) / (2(10)3+1024)) = 10.08…
Hence, 10.08… is the approximate cubic root of 1024.
Common Mistakes and How to Avoid Them in the Cube Root of 1024
Understanding common misconceptions or mistakes can make your calculations error free. So let us see how to avoid those from happening.
Mistake 1
For β1024, 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).
Mistake 2
Applying exponent rules incorrectly when finding cube roots.
β1024 is not same as 10243. β1024 = 10.079… and 10243 is something very large quantity.
For large non-perfect cubes, students frequently estimate wrongly and leave it with a wrong result.
Keep the methods of finding cube roots in front whenever attempting large non-perfect cubes.
Mistake 4
Students typically rely on memorizing rather than understanding concepts of cube root.
Memorizing is not the solution when it comes to complex problems. So understanding the methods of finding cube roots is advisable.
Mistake 5
Misapply the cube root property like when asked to solve β(1024)3, students might do as β(1024×3)
Clear the concepts again and again if they don’t understand, where to do what. β(1024)3≠β(1024×3). β(1024)3= 1024
Cube Root of 1024 Examples
Problem 1
Find (β512/ β1024) Γ (β512/ β1024) Γ (β512/ β1024)
(β512/ β1024) × (β512/ β1024) × (β512/ β1024)
= (β512× β512× β512) / (β1024× β1024× β1024)
=((512)β
)3/ ((1024)β
)3
=512/1024
=1/2
Answer: 1/2
Explanation
We solved and simplified the exponent part first using the fact that, β512=(512)β
and β1024=(1024)β
, then solved.
Problem 2
If y = β1024, find yΒ³/ yβΆ
y=β1024
⇒ y3/y6= (β1024)3 / (β1024)6
⇒ y3/y6= 1024/ (1024)2= 1/1024
Answer: 1/1024
Explanation
(β1024)3=(10241/3)3=1024, and β(1024)6=(10241/3)6=(1024)2. Using this, we found the value of y3/y6.
Problem 3
Multiply β1024 Γ β1000
β1024×β1000
= 10.07×10
=100.7
Answer: 100.7
Explanation
We know that the cubic root of 1000 is 10, hence multiplying β1000 with β1024.
Problem 4
Solve the equation: (x)Β³/Β²=1024
(x)3/2=1024
⇒ (x)1/2=(1024)1/3
⇒ (x)1/2 = 10.07
⇒ (x) = (10.07)2
⇒ x= 101.4049
Answer: 101.4049
Explanation
Simplified the equation applying the cube root features and found the answer.
Problem 5
Find 1000aΒ³bβΆ/1331aβΆbΒ³
1000a3b6/1331a6b3
= (10ab2)3/(11a2b)3
= 10b3/11a3
Answer: 10b3/11a3
Explanation
Simplified the given expression using exponential rules.
FAQs on 1024 Cube Root
1.What is the nearest cube to 1024?
2.What is the square root of 1024?
3.What is β1024 simplified ?
4.How to simplify the cube root of 1024?
5.s 1024 a real number?
Important Glossaries for Cube Root of 1024
- 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.
- Approximation - Finding out a value which is near to the correct answer, but not perfectly correct.
- Iterative method - This method is a mathematical process which uses an initial value to generate a further sequence of solutions for a problem, step-by-step.
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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.
