Cube Root by Successive Subtraction
Cube Root by Successive Subtraction
Like squares of natural numbers, cubes too have some interesting patterns.
.
.
.
Also
From the above pattern, we see that is the sum of the first two numbers of the sequence 1,7,19.37,...Similarly,
is the sum of the first three numbers and so on.In short,these numbers(1,7,19,...)may be obtained by putting n=1,2,3,...in 1+n(n-1) X 3
Thus to find the cube root of a given number, we go on subtracting the numbers of the sequence 1,7,19,37,... till we get a zero. The number of subtractions needed for this purpose is the cube root of the given number.
Illustration: Find the cube root of 343 by successive subtraction.
Solution: Subtract the numbers of the sequence 1,7,19,37,...from 343 till we get zero.
343-1=342
342-7=335
335-19=316
316-37=279
279-61=218
218-91=127
127-127=0
Since we have subtracted seven times to get 0, Hence
Illustration: Find the cube root of 216 by successive subtraction.
While finding the cube root of 729 using the successive subtraction method, find the number obtained after subtraction in 5th step. | |||
| Right Option : B | |||
| View Explanation | |||
What is the number obtained in the third step while finding the cube root of 216 by successive subtraction? | |||
| Right Option : C | |||
| View Explanation | |||
Find the cube root of 64 by successive subtraction of numbers 1,7,19,37,... | |||
| Right Option : A | |||
| View Explanation | |||
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