Find the nearest integer to the cube root of each of the following. (

1.	Find the nearest integer to the cube root of each of the following. (i) 331776 (ii) 46656 (iii) 373248
Answer» (i) 331776 60³ = 216000 < 331776 < 343000 = 70³ Hence \(3\sqrt{331776}\) lies between 60 and 70. We do not know whether 331776 in a perfect cube or not. However we may sharpen the bound. 68³ = 314432, 69³ = 328509 Hence \(3\sqrt{331776}\) lies between 69 and 70 331776 – 328509 = 3267 343000 – 331776= 11224 331776 in nearer to 69³ ∴ The closest integer to \(3\sqrt{331776}\) is 69. (ii) 46656 30³ = 2700 < 46656 < 64000 – 40³ \(3\sqrt{46656}\) lies between 30 and 40 we do not know whether 46656 in a perfect cube or not. However we may sharper the bound 35³ = 42875, 36³ = 46656 ∴ \(3\sqrt{46656}\) = 36 (iii) 373248 70³ = 343000 < 373248 < 512000 – 80³ \(3\sqrt{373248}\) lies between 70 and 80. We do not know whether 373248 is a perfect cube or not. However we may sharpen the bound. 71³ = 357911, 72³ = 373248 ∴ \(3\sqrt{373248}\) = 72

Find the nearest integer to the cube root of each of the following. (i) 331776 (ii) 46656 (iii) 373248

Answer»

(i) 331776

60³ = 216000 < 331776 < 343000 = 70³

Hence \(3\sqrt{331776}\) lies between 60 and 70.

We do not know whether 331776 in a perfect cube or not.

However we may sharpen the bound.

68³ = 314432, 69³ = 328509

Hence \(3\sqrt{331776}\) lies between 69 and 70

331776 – 328509 = 3267

343000 – 331776= 11224

331776 in nearer to 69³

∴ The closest integer to \(3\sqrt{331776}\) is 69.

(ii) 46656

30³ = 2700 < 46656 < 64000 – 40³

\(3\sqrt{46656}\) lies between 30 and 40 we do not know whether 46656 in a perfect cube or not.

However we may sharper the bound

35³ = 42875, 36³ = 46656

∴ \(3\sqrt{46656}\) = 36

(iii) 373248

70³ = 343000 < 373248 < 512000 – 80³

\(3\sqrt{373248}\) lies between 70 and 80.

We do not know whether 373248 is a perfect cube or not.

However we may sharpen the bound.

71³ = 357911, 72³ = 373248

∴ \(3\sqrt{373248}\) = 72