Question

find the cube root of 17576 without factorization

Answer 1

as we will first groups total is it int o two parts as 3 places from left to right. the 1st group will contain the no 576 and the 2nd group will contain the no 17.then through the process of estimation the cube root of 576 will be 6. so we got ones place of the required cube root no as 6.then in 2nd group, 16 comes between 2cube that is 8 and 3cube that is 27 .so we will take the smaller no .that is 2as tens place.the no obtained is 26

Answer 2

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Solution:-

Step 1 - Units digit of 17576 is 6 as per the tip given

.. Units digit of 3√17/576 is 6

Step II- Striking out or leave last three digits from the right i.e. 576.

Factors of 17/576 are

Step III- The number left is 17 and 17 lies between 2square3 and 3square3

2square3 < 17 < 3square3

Step IV- The possible number whose cube is less than 17 is 2.

Thus ten's digit of 3√17576 is 2.

(｡◕o◕｡) 3√17576 = 26