Question

Find the cube root of 343 using the successive subtraction method

Answer 1

Method of successive subtraction to find the cube root:
We Subtract the numbers 1, 7 ,19 ,37, 61, 91, 27 169........ Successively till we get zero.
The number of subtractions will give the cube root of the number.
The number 1, 7, 19, 37, 61, 91, 127, 169....... are obtained by putting n= 1,2,3...... in 1+n×(n-1)×3
For e.g:Find the cube root of 125
125-1=124
124-7=117
1117- 19=98
98- 37=61
61-61=0
The number of subtractions to get zero is 5³√125= 5_____________________________Hope this will help you...

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Answer 2

Answer:

7

Step-by-step explanation:

343-1=342, (1)

342-7=335, (2)

335-19=316, (3)

316-37=279, (4)

279-61=218, (5)

218-91=127, (6)

127-127=0. (7)

Since we had to successively subtract 343 7 times,

Therefore,

$\sqrt[3]{343} = 7$

Hope it helps.