How ti find cube root of 9261 by long division method?

Answer 1

To find the cube root of 9261 using the long division method, start by grouping the digits of 9261 into sets of three from the right, yielding 9 and 261. Next, find the largest cube less than or equal to 9, which is (2^3 = 8), and place 2 as the first digit of the cube root. Subtract 8 from 9, bringing down the next group (261) to get 1261. For the next step, double the current quotient (2) to get 4, and find a digit (x) such that (4x \times x^2) is less than or equal to 1261; here, (x = 7) works, as (47 \times 7^2 = 47 \times 49 = 2303) is too high. Continue this process to refine the next digits until reaching the desired precision. The final result gives the cube root of 9261 as 21.