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Find the cube root of the following by looking at the last digit and using estimation

(i) 91125

(ii) 166375

(iii) 704969

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(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 43 = 64 < 91 < 125 = 53 

Hence 403 = 64000 <91125 < 125000 = 503 

∴ 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. 

53 = 125 < 166 < 216 = 63 

Hence 503 = 125000, < 166375 < 216000 = 603 

\(3\sqrt{166375}\) 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 

83 = 512 < 704 < 729 – 93 

Hence = 803= 512000 < 704969 < 72900 = 903

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

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

\(3\sqrt{704969}\)  = 89

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