Using the method of successive subtraction examine whether or not the

1.	Using the method of successive subtraction examine whether or not the following numbers are perfect cubes:(i) 792(ii) 1331
Answer» (i) 792 792 – 1 = 791 791 – 7 = 784 784 – 19 = 765 765 – 37 = 728 728 – 61 = 667 667 – 91 = 576 576 – 127 = 449 449 – 169 = 280 280 – 217 = 63 Other number to be subtracted is 271, which is greater than 63 ∴ 792 is not a perfect cube (ii) 1331 1331 – 1 = 1330 1330 – 7 = 1323 1323 – 19 = 1304 1304 – 37 = 1267 1267 – 61 = 1206 1206 – 91 = 1115 1115 – 127 = 988 988 – 169 = 819 819 – 217 = 602 602 – 271 = 331 331 – 331 = 0 Here ,subtraction is performed 11 times Cube root of 1331 is 11 ∴ 1331 is a perfect cube.

Using the method of successive subtraction examine whether or not the following numbers are perfect cubes:(i) 792(ii) 1331

Answer»

(i) 792

792 – 1 = 791

791 – 7 = 784

784 – 19 = 765

765 – 37 = 728

728 – 61 = 667

667 – 91 = 576

576 – 127 = 449

449 – 169 = 280

280 – 217 = 63

Other number to be subtracted is 271, which is greater than 63

∴ 792 is not a perfect cube

(ii) 1331

1331 – 1 = 1330

1330 – 7 = 1323

1323 – 19 = 1304

1304 – 37 = 1267

1267 – 61 = 1206

1206 – 91 = 1115

1115 – 127 = 988

988 – 169 = 819

819 – 217 = 602

602 – 271 = 331

331 – 331 = 0

Here ,subtraction is performed 11 times

Cube root of 1331 is 11

∴ 1331 is a perfect cube.