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

1.	Find the cube root of the following by looking at the last digit and using estimation(i) 91125(ii) 166375(iii) 704969
Answer» (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

Find the cube root of the following by looking at the last digit and using estimation(i) 91125(ii) 166375(iii) 704969

Answer»

(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