Question

3. Estimate the cube root of each of the following perfect cubes using full explanation.
(1) 405224
(ii) 3375
(iii) 238328
(iv) 54872
(v) 2197​

Answer 1

Step-by-step explanation:

1)we can write 405224=8×50653

405224=(2×2×2)×(37×37×37)

405224=(2)³×(37)³

taking cube both sides

³√405224=³√(2)³×(37)³

³√405224=2×37

³√405224=74

2)

3375=(5)³×(3)³

taking cube root both sides

³√3375=(5)³×(3)³

³√3375=3×5

³√3375=15

3)

238328=8×29791

238328=(2)³×(31)³

taking cube both sides

³√238328=³√(2)³×(31)³

³√238328=2×31

³√238328=62

4)

54872=(2)³×(19)³

taking cube root both sides

³√54872=³√(2)³×(19)³

³√54872=2×19

³√54872=38

5)

2197=(13)³

taking cube root both sides

³√2197=³√(13)³

³√2197=13

Answer 2

ANSWER

1. 405224=74
2. 3375=15
3. 238328=62
4. 54872=38
5. 2197=13

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