Last updated on May 26th, 2025
The cube root of 7 is the value that, when multiplied by itself three times (cubed), gives the original number 7. Do you know? Cube roots apply to our real life also, like that for measuring volume and scaling, density and mass calculation, etc.
The cube root of 7 is 1.91293118277. The cube root of 7 is expressed as ∛7 in radical form, where the “∛" sign is called the “radical” sign. In exponential form, it is written as (7)â…“. If “m” is the cube root of 7, then, m3=7. Let us find the value of “m”.
The Prime Factorization of 7 is 7, so, the cube root of 7 is expressed as ∛7 as its simplest radical form. We can find cube root of 7 through another 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 ∛a≅ 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 7.
Step 1: Let a=7. Let us take x as 1, since, 1 is the nearest perfect cube which is less than 7.
Step 2: Apply the formula. ∛7≅ 1((13+2×7) / (2(1)3+7))=15/9 ≅ 1.667
Hence, 1.667 is the approximate cubic root of 7.
some common mistakes and their solutions are given below:
Find ∛7 / ∛8
∛7/ ∛8= 1.913 / 2 =0.9565
Answer: 0.9565
We know that the cubic root of 8 is 2, hence dividing ∛7 by 2.
The Volume of a cube is 7 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 = ∛(Volume of the cube)
⇒side of the cube = ∛7
⇒ side of the cube = 1.913 cm
Answer: 1.913 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 ∛7 - ∛8
∛7-∛8= 1.913–2= -0.087
Answer: -0.913
We know that the cubic root of 8 is 2, hence subtracting ∛8 from ∛7.
What is ∛(7² ) ?
∛(72) = ∛49 = 3.659…
Answer: 3.659…
We first found the square value of 7, which is 49, and then found out the cube root of 49.
Find ∛(7+1).
∛(7+1) = ∛8=2
Answer: 2
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.
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