Kl. Find the cube root by using the estimation method.
(a) 2,38,328
(b) -1,75,616
(c) 6,300
(d) 24,567
(e) 5,832
(f) 10,648
(g) 3,00,763
Plz Answer all questions
Answers
Answer:
(a)
238328
Grouping the 3 digits from the right, we get two groups,
238 and 328
II: unit digit of cube root will be 2 since 8 is the unit digit of cube.
III: 63=216,73=343
Ten's digit =6
Cube root =62.
(b) The cube root of 17576 is 26.
(c) 18 is the cube root of 6,300.
(d) 23 is the cube root of 24,567.
(e) For calculating the cube root of 5832, this number has to be separated in two group, i.e. 3 and 832.
considering the group 832:
832 ends with 2 and we know that if digit 2 is at the end of any perfect cube number, then its cube root will have 8 at its unit place only. Therefore, the digits at the units place of the required cube root is taken as 8.
Now consider the other group 3:
We know that the 13=1 and 23=8
Also, 1<5<8
So, 1 will be taken at the tens place. So, the required cube root of 5832 is 18.
35832=18
(f) Let us consider the given number as two groups starting from the unit digit.
Here the groups are: 648 which is the first group and 10 which is the second group.
From the first group, we calculate the unit digit.
The unit digit of 648 is 8 = 23.
Therefore the unit digit of our required number is 2.
Now consider the second group for the 10s digit,
8 < 10 <27
i.e., 23 < 10 < 33
As the smallest number is 2, it becomes the tens place of the required cube root.
So, 3√10648 = 22