Class maths students are Interesting.all the best guy for you homework

1. Question 1.
Find the cube roots of each of the following integers :
(i) -125
(ii) -5832
(iii) -2744000
(iv) -753571
Solution:

3. Question 2.
Show that :
Solution:

5. Question 3.
Find the cube root of each of the following numbers :
(i) 8 x 125
(ii) -1728 x 216
(iii) -27 x 2744
(iv) -729 x -15625
Solution:

7. Question 4.
Evaluate :
Solution:

8. Question 5.
Find the cube root of each of the following rational numbers.
Solution:

12. Question 6.
Find the cube root of each of the following rational numbers :
(i) 0.001728
(ii) 0.003375
(iii) 0.001
(iv) 1.331
Solution:

14. Question 7.
Evaluate each of the following :

15. Solution:

17. Question 8.
Show that :

18. Solution:

19. Question 9.
Fill in the Blanks :

20. Solution:

23. Question 10.
The volume of a cubical box is 474.552 cubic metres. Find the length of each
side of the box.
Solution:
Question 11.
Three numbers are to one another 2:3: 4. The sum of their cubes is 0.334125.
Find the numbers.
Solution:

24. Question 12.
Find side of a cube whose volume is

25. Solution:
Question 13.
Evaluate :
Solution:

27. Question 14.
Find the cube root of the numbers : 2460375,20346417,210644875,57066625
using the fact that
(i) 2460375 = 3375 x 729

28. (i) 20346417 = 9261 x 2197
(iii) 210644875 = 42875 x 4913
(iv) 57066625 = 166375 x 343
Solution:

29. Question 15.
Find the units digit of the cube root of the following numbers ?
(i) 226981
(ii) 13824
(iii) 571787
(iv) 175616
Solution:
(i) 226981
In it unit digit is 1
∴The units digit of its cube root will be = 1
(∵ 1 x 1 x 1 = 1)
∴Tens digit of the cube root will be = 6

30. (ii) 13824
∵ The units digit of 13824 = 4
(∵ 4 X 4 X 4 = 64)
∴Units digit of the cube root of it = 4
(iii) 571787
∵ The units digit of 571787 is 7
∴The units digit of its cube root = 3
(∵ 3 x 3 x 3 = 27)
(iv) 175616
∵ The units digit of 175616 is 6
∴The units digit of its cube root = 6
(∵ 6 x 6 x 6=216)
Question 16.
Find the tens digit of the cube root of each of the numbers in Question No. 15.
Solution:
(i) In 226981
∵ Units digit is 1
∴Units digit of its cube root = 1
We have 226
(Leaving three digits number 981)
63
= 216 and 73
= 343
∴63
∠226 ∠ T
∴The ten’s digit of cube root will be 6
(ii) In 13824
Leaving three digits number 824, we have 13
∵ (2)3
= 8, (3)3
= 27
∴23
∠13 ∠3′
∴Tens digit of cube root will be 2
(iii) In 571787
Leaving three digits number 787, we have 571
83
= 512, 93
= 729
∴ 83
∠571 ∠93
Tens digit of the cube root will be = 8
(iv) In 175616
Leaving three digit number 616, we have 175
∵ 53
= 125, 63
= 216
∴53
∠175 ∠63
∴Tens digit of the cube root will be = 5