# Find the cube root of the following by looking at the last digit and using estimation (i) 91125

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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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