Find the smallest number that must be subtracted from those of the num

1.	Find the smallest number that must be subtracted from those of the numbers in question 2 which are not perfect cubes, to make them perfect cubes. What are the corresponding cube roots?
Answer» In previous question there are three numbers which are not perfect cubes. (i) 130 Apply subtraction method, 130 – 1 = 129 129 – 7 = 122 122 – 19 = 103 103 – 37 = 66 66 – 61 = 5 ∵ Next number to be subtracted is 91, which is greter than 5 Hence, 130 is not a perfect cube. So, to make it perfect cube we subtract 5 from it. 130 – 5 = 125 (which is a perfect cube of 5) (ii) 345 Apply subtraction method, 345 – 1 = 344 344 – 7 = 337 337 – 19 = 318 318 – 37 = 281 281 – 61 = 220 220 – 91 = 129 129 – 127 = 2 ∵ Next number to be subtracted is 169, which is greter than 2 Hence, 345 is not a perfect cube. So, to make it a perfect cube we subtract 2 from it. 345 – 2 = 343 (which is a perfect cube of 7) (iii) 792 Apply subtraction method, 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 ∵ Next number to be subtracted is 271, which is greter than 63 Hence, 792 is not a perfect cube. So, to make it a perfect cube we subtract 63 from it. 792 – 63 = 729 (which is a perfect cube of 9)

Find the smallest number that must be subtracted from those of the numbers in question 2 which are not perfect cubes, to make them perfect cubes. What are the corresponding cube roots?

Answer»

In previous question there are three numbers which are not perfect cubes.

(i) 130

Apply subtraction method,

130 – 1 = 129

129 – 7 = 122

122 – 19 = 103

103 – 37 = 66

66 – 61 = 5

∵ Next number to be subtracted is 91, which is greter than 5

Hence, 130 is not a perfect cube. So, to make it perfect cube we subtract 5 from it.

130 – 5 = 125 (which is a perfect cube of 5)

(ii) 345

Apply subtraction method,

345 – 1 = 344

344 – 7 = 337

337 – 19 = 318

318 – 37 = 281

281 – 61 = 220

220 – 91 = 129

129 – 127 = 2

∵ Next number to be subtracted is 169, which is greter than 2

Hence, 345 is not a perfect cube. So, to make it a perfect cube we subtract 2 from it.

345 – 2 = 343 (which is a perfect cube of 7)

(iii) 792

Apply subtraction method,

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

∵ Next number to be subtracted is 271, which is greter than 63

Hence, 792 is not a perfect cube. So, to make it a perfect cube we subtract 63 from it.

792 – 63 = 729 (which is a perfect cube of 9)