Question

find cube root by estimation method of 46656​

Answer 1

Solution

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Step I. Make groups of three digits starting from unit place digit as 46 656

Step II. 1st group is 656. Its unit place digit is 6 which is obtained by the cube of any number having unit place digit as 6. We know that 63 = 216

Step III. Second group is 46.

• 33 < 46 < 43

∴ Ten place digit is 3

Hence, cube root of 46656 is 36

∴³√46656 = 36

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Answer 2

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⚘The cube root of 46656 by estimating method is 36.

$\huge\fcolorbox{black}{magenta}{⚘★step \: by step \: explaination᭄✍︎⚘}$

• ⚘Resolving 46656 into Prime factors (follow the attachment for it)
• ⚘Step I. Make groups of three digits starting from unit place digit as 46656.
• ⚘Step II. 1st group is 656. Its unit place digit is 6 which is obtained by the cube of any number having unit place digit as 6.
• ⚘We know that 63 = 216.
• ⚘Step III. Second group is 46.
• ⚘33 < 46 < 43
• ⚘∴ Ten place digit is 3
• ⚘Hence, cube root of 46656 is 36
• ⚘∴³√46656 = 36

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