Question

Find the cube root of 389017 by finding their units and digits
A. 63
B. 67
C. 73
D. 77

Answer 1

Hint: We can find cube root by unit digits. First we take the unit digit of the given number. Then we find the cube of that digit. Last digit of the cube will represent the last digit of the required cube root. For finding tenth digit of cube digit we ignore next two digit from unit digit and then we check the remaining number lies between the cube of which two numbers. We always consider that digit whose cube is closer to the remaining number.

Complete step by step solution:
Given number is 389017.
Last digit is 7.
So cube of 7 is ${{7}^{3}}=343$
So the last digit of cube root of 389017 is 3.
Now we can ignore the next two digits to the unit digit.
So we will get a number as 389.
Let, us check the perfect cube which is near to 389it should be less than 389
${{1}^{3}}=1$
${{2}^{3}}=8$
${{3}^{3}}=27$
.
.
${{7}^{3}}=343$
${{8}^{3}}=512$
Hence $343<389<512$
So we can say 389 lies between cube of 7 and 8 but it is more close to cube of 7 compared to cube of 8.
Hence 7 is the tens digit in the cube root of 389017 because 389 is slightly less than from cube of 7.
So required cube root of 389017 is 73
Hence, option (C) is correct.

Note: To find the tens digit of cube root ignore the next two digits to units digit .
For example, here we have ignored 01 in the number 389017 and used 389 to find the tenth digit of cube root.