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 1024, and its examples.
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”.
We can find cube roots of 1024 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 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.
Understanding common misconceptions or mistakes can make your calculations error free. So let us see how to avoid those from happening.
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
We solved and simplified the exponent part first using the fact that, β512=(512)β
and β1024=(1024)β
, then solved.
If y = β1024, find yΒ³/ yβΆ
y=β1024
⇒ y3/y6= (β1024)3 / (β1024)6
⇒ y3/y6= 1024/ (1024)2= 1/1024
Answer: 1/1024
(β1024)3=(10241/3)3=1024, and β(1024)6=(10241/3)6=(1024)2. Using this, we found the value of y3/y6.
Multiply β1024 Γ β1000
β1024×β1000
= 10.07×10
=100.7
Answer: 100.7
We know that the cubic root of 1000 is 10, hence multiplying β1000 with β1024.
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
Simplified the equation applying the cube root features and found the answer.
Find 1000aΒ³bβΆ/1331aβΆbΒ³
1000a3b6/1331a6b3
= (10ab2)3/(11a2b)3
= 10b3/11a3
Answer: 10b3/11a3
Simplified the given expression using exponential rules.
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.
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