Can you find the cube root??

Algebra Level 1

Find the cube root of

1030301. 1030301.

(Please don't use a calculator.I will tell you a trick by which you can find cube root of any number.)


The answer is 101.

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1 solution

Sunil Pradhan
Jul 24, 2014

1030301 make groups of 3 digits from the end (1)(030)(301)

as cube is ending with 1, cube root also ends with 1

consider 1st group (1) it is cube of 1 so cube root of 1030301 is 1x1

consider cube of 100 = 1000000 it is near to 103030 so its cube root is nearer to 100 and is 101

similar to finding out approximate square root we are making groups of 2 digits from the end.

e.g. 9804 the groups of 2 digits from the end are written in bracket (98)(04) as the number is ending with 4, the square root of number is either ending with 2 (as 2 × 2 = 4) or 8 (as 8 × 8 = 64 4 in unit place)

Now consider first group (98) find number whose square is 98 or less than 98 (as 98 is not a square number) so such number is 9 (9 × 9 = 81 < 98)

so your square root is either 92 or 98 you must know some shortcuts to find square of number. such as square of number ending with 1 or 5

95² = 9025 our number is 9804 which is > than 9025 so square root is 98.

similarly in case of cube root make group of 3 digits from the end (unit place) number is 1030301 so groups are (1)(030)(301)) so cube root considering group (301) end with 1 as 1³

consider first group (1) consider the group, find a number whose cube is equal to the number in the group or less than the number in this case it is 1

so answer is of 3 digits say 1 X 1 find 100³ = 1000000 so answer is nearer to 100 try 101³ = (100 + 1)³ = (100³ + 3× 100× 1(100 + 1) + 1³ = 1030301

Sunil Pradhan - 6 years, 10 months ago

Not a perfect idea. :-(

Vinod Chhallany - 6 years, 10 months ago

It's not clear.I did n't understand. Please,Can you explain it in another way

adilakshmi marasu - 6 years, 10 months ago

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