RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-5) | RD Sharma Solutions for Class 8 Mathematics PDF Download

Question 1: Making use of the cube root table, find the cube roots 7

Answer 1: Because 7 lies between 1 and 100, we will look at the row containing 7 in the column of x.
By the cube root table, we have: 

 1.913

Thus, the answer is 1.913. 

Question 2: Making use of the cube root table, find the cube root 70

Answer 2: Because 70 lies between 1 and 100, we will look at the row containing 70 in the column of x.
By the cube root table, we have: 

 4.121

Question 3: Making use of the cube root table, find the cube root 700

Answer 3: We have: 

700=70×10700=70×10
∴∴ Cube root of 700 will be in the column of   against 70. 

By the cube root table, we have: 

 =8.879

Thus, the answer is 8.879. 

Question 4: Making use of the cube root table, find the cube root 7000

Answer 4: We have: 

7000=70×1007000=70×100

By the cube root table, we have:  

 =1.913×10=19.13 

Question 5: Making use of the cube root table, find the cube root 1100

Answer 5: We have: 

1100=11×1001100=11×100

By the cube root table, we have:  

 =2.224×4.642=10.323 (Up to three decimal places)11003=113×1003=2.224×4.642=10.323 (Up to three decimal places)

Thus, the answer is 10.323. 

Question 6: Making use of the cube root table, find the cube root 780

Answer 6: We have: 

780=78×10780=78×10

∴∴ Cube root of 780 would be in the column of  against 78. 

By the cube root table, we have: 

 = 9.205

Thus, the answer is 9.205. 

Question 7: Making use of the cube root table, find the cube root 7800

Answer 7: We have: 

7800=78×1007800=78×100

By the cube root table, we have: 

 =4.273×4.642=19.835 (upto three decimal places) 

Thus, the answer is 19.835 

Question 8: Making use of the cube root table, find the cube root 1346 

Answer 8: By prime factorisation, we have: 

1346=2×673⇒ 

Also 

670<673<680⇒

From the cube root table, we have: 

For the difference (680−-670), i.e., 10, the difference in the values 

=8.794−8.750=0.044=8.794-8.750=0.044

∴∴ For the difference of (673−-670), i.e., 3, the difference in the values 

 ×3=0.0132=0.013=0.04410×3=0.0132=0.013 (upto three decimal places) 

 =8.750+0.013=8.7636733=8.750+0.013=8.763

Now 

 =1.260×8.763=11.04113463=23×6733=1.260×8.763=11.041 (upto three decimal places) 

Thus, the answer is 11.041. 

Question 9: Making use of the cube root table, find the cube root 250

Answer 9: We have: 

250=25×100250=25×100

∴∴ Cube root of 250 would be in the column of  against 25. 

By the cube root table, we have: 

Thus, the required cube root is 6.3. 

Question 10: Making use of the cube root table, find the cube root 5112

Answer 10: By prime factorisation, we have: 

5112=23×32×71⇒ 

By the cube root table, we have: 

 =2×2.080×4.141=17.22751123=2×93×713=2×2.080×4.141=17.227 (upto three decimal places) 

Thus, the required cube root is 17.227. 

Question 11: Making use of the cube root table, find the cube root
9800 

Answer 11: We have: 

9800=98×1009800=98×100

By cube root table, we have:  

 =4.610×4.642=21.4098003=983×1003=4.610×4.642=21.40 (upto three decimal places) 

Thus, the required cube root is 21.40. 

Question 12: Making use of the cube root table, find the cube root 732

Answer 12: We have: 

730<732<740⇒ 

From cube root table, we have: 

For the difference (740−-730), i.e., 10, the difference in values 

=9.045−9.004=0.041=9.045-9.004=0.041

∴∴ For the difference of (732−-730), i.e., 2, the difference in values 

 2=0.0082

 =9.004+0.008=9.012

Question 13: Making use of the cube root table, find the cube root 7342

Answer 13: We have: 

7300<7342<7400⇒ 

From the cube root table, we have:  

For the difference (7400−-7300), i.e., 100, the difference in values 

=19.48−19.39=0.09 

∴∴ For the difference of (7342−-7300), i.e., 42, the difference in the values 

 ×42=0.0378=0.037 

  =19.39+0.037=19.427 

Question 14: Making use of the cube root table, find the cube root 133100

Answer 14: We have: 

133100=1331×100⇒ 

By cube root table, we have:  

 =4.6421003=4.642

 =11×4.642=51.062 

Question 15: Making use of the cube root table, find the cube root 37800

Answer 15: We have: 

37800=23×33×175⇒ 

Also 

170<175<180⇒ 

From cube root table, we have:  

For the difference (180−-170), i.e., 10, the difference in values 

=5.646−5.540=0.106=5.646-5.540=0.106

∴∴ For the difference of (175−-170), i.e., 5, the difference in values 

 ×5=0.053=0.10610×5=0.053

 =5.540+0.053=5.5931753=5.540+0.053=5.593

Now 

37800=6×  =6×5.593=33.55837800=6×1753=6×5.593=33.558

Thus, the required cube root is 33.558. 

Question 16: Making use of the cube root table, find the cube root 0.27

Answer 16: The number 0.27 can be written as 27/100.

Now 

By cube root table, we have:  

 
=0.6460.273=31003=34.642=0.646.

Thus, the required cube root is 0.646. 

Question 17: Making use of the cube root table, find the cube root 8.6

Answer 17: The number 8.6 can be written as 86/10.

Now 

By cube root table, we have: 

 2.0498.63=863103=4.4142.154=2.049

Thus, the required cube root is 2.049. 

Question 18: Making use of the cube root table, find the cube root 0.86

Answer 18: The number 0.86 could be written as 86/100.

Now 

By cube root table, we have:  

 =0.9510.863=8631003=4.4144.642=0.951 (upto three decimal places)

Thus, the required cube root is 0.951. 

Question 19: Making use of the cube root table, find the cube root 8.65

Answer 19: The number 8.65 could be written as 865/100.

Now 

Also 

860<865<870⇒ 

From the cube root table, we have:  

For the difference (870−-860), i.e., 10, the difference in values 

=9.546−9.510=0.036=9.546-9.510=0.036
∴∴ For the difference of (865−-860), i.e., 5, the difference in values
 ×5=0.018  (upto three decimal places) 

 9.510+0.018=9.5288653=9.510+0.018=9.528 (upto three decimal places) 

From the cube root table, we also have: 

 2.0538.653=86531003=9.5284.642=2.053 (upto three decimal places) 

Thus, the required cube root is 2.053. 

Question 20: Making use of the cube root table, find the cube root 7532

Answer 20: We have: 

7500<7532<7600⇒ 

From the cube root table, we have:  

For the difference (7600−-7500), i.e., 100, the difference in values 

=19.66−19.57=0.09=19.66-19.57=0.09

∴∴ For the difference of (7532−-7500), i.e., 32, the difference in values 

 ×32=0.0288=0.029=0.09100×32=0.0288=0.029 (up to three decimal places) 

 =19.57+0.029=19.59975323=19.57+0.029=19.599 

Question 21: Making use of the cube root table, find the cube root
833 

Answer 21: We have: 

830<833<840⇒ 

From the cube root table, we have:  

For the difference (840−-830), i.e., 10, the difference in values 

=9.435−9.398=0.037=9.435-9.398=0.037

∴∴ For the difference (833−-830), i.e., 3, the difference in values 

 ×3=0.0111=0.011=0.03710×3=0.0111=0.011 (upto three decimal places) 

 =9.398+0.011=9.4098333=9.398+0.011=9.409 

Question 22: Making use of the cube root table, find the cube root 34.2

Answer 22: The number 34.2 could be written as 342/10.

Now 

Also 

340<342<350⇒ 

From the cube root table, we have: 

For the difference (350−-340), i.e., 10, the difference in values 

=7.047−6.980=0.067=7.047-6.980=0.067. 

∴∴ For the difference (342−-340), i.e., 2, the difference in values 

 ×2=0.013=0.06710×2=0.013  (upto three decimal places) 

 =6.980+0.0134=6.9933423=6.980+0.0134=6.993 (upto three decimal places) 

From the cube root table, we also have: 

 3.246 

Thus, the required cube root is 3.246. 

Question 23: What is the length of the side of a cube whose volume is 275 cm³. Make use of the table for the cube root.

Answer 23: Volume of a cube is given by:  

V=a3V=a3, where a = side of the cube  

∴∴ Side of a cube = a= 

If the volume of a cube is 275 cm³, the side of the cube will be 

We have: 

270<275<280⇒

From the cube root table, we have:  

For the difference (280−-270), i.e., 10, the difference in values 

=6.542−6.463=0.079=6.542-6.463=0.079

∴∴ For the difference (275−-270), i.e., 5, the difference in values 

 ×5=0.0395  ≃ 0.04=0.07910×5=0.0395  ≃ 0.04 (upto three decimal places) 

 =6.463+0.04=6.5032753=6.463+0.04=6.503 (upto three decimal places)

Thus, the length of the side of the cube is 6.503 cm.