(i) 91125

Unit digit of 91125 in 5.

Therefore the units digit in its cube root is 5.

Let us split 91125 as 91 and 125. We find that 4^{3} = 64 < 91 < 125 = 5^{3}

Hence 40^{3} = 64000 <91125 < 125000 = 50^{3}

∴ Cube root of 91125 lies between 40 and 50 and units digit is 5 the only such number is 45.

∴ \(3\sqrt{91125} = 45\)

(ii) 166375

Units digit of 166375 is 5.

Therefore the units digit of its cube root is 5.

Let us split 166375 as 166 and 375.

5^{3} = 125 < 166 < 216 = 6^{3}

Hence 50^{3} = 125000, < 166375 < 216000 = 60^{3}

∴ \(3\sqrt{166375}\) lies between 50 and 60.

Since the units digit is 5 the only such number in 55

∴ \(3\sqrt{166375}\) = 55

(iii) 704969

The units digit of 704969 is 9. Therefore the units digits of its cube root are 9.

Let us split 704969 as 704 and 969

8^{3} = 512 < 704 < 729 – 9^{3}

Hence = 80^{3}= 512000 < 704969 < 72900 = 90^{3}

∴ \(3\sqrt{704969}\) lies between 80 and 90.

Since the units digits is 9 the only such number is 89.

∴ \(3\sqrt{704969}\) = 89