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Find the cube root of number 120.
A) 4.1
B) 4.2
C) 4.7
D) 4.9

Answer
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Hint: We will use the Babylonian Algorithm for cube roots to determine the result. The Babylonian Algorithm for cube roots is given by xn+1=(2xn+(Nxn2))3.
where N is the number for which cube root is to be found
xn​ is the initial approximation of the cube root
xn+1​ is the subsequent improvement on the cube root.

Complete step-by-step answer:
We have to find out the cube root of 120.
We use the Babylonian Algorithm for cube roots here,
According to the algorithm, the cube root is given by the formula
xn+1=(2xn+(Nxn2))3
where N is the number for which cube root is to be found
xn​ is the initial approximation of the cube root
xn+1​ is the subsequent improvement on the cube root.
In the question of our case,
N=120
x0=4
Since,  43<120<53
Substituting all the above values we get the required expression as,


x1=((2)(4)+(12042)3)x1=(8+(12016)3)x1=4.9
Similarly, x2 can be determined by,
x2=((2)(4.9)+(120(4.9)2)3)x2=(9.8+(12024.01)3)x2=9.8+4.993x2=4.9
We can see the value stabilizes around 4.9.
Therefore, the cube root of 120, is obtained as 4.9.
Matching from the give options we get, the cube root of 120 is 4.9, that is option (D).

Note: The possibility of error in this question can be restricted to the value of only x1 and not x2 also which would be wrong. Always go for determining both the values then arrive at the final answer.