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Q.

Find the cube root of 27000.

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a

20

b

30

c

28

d

25

answer is B.

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Detailed Solution

We have to find the cube root of 27000. We will first factor it by 2.
27000= 2×13500
We can again factor 13500 by 2,
27000= 2×2×6750
Again, factoring 6750 by 2, we get
27000= 2×2×2×3375
Now, we will factor 3375 by 5.
27000= 2×2×2×5×675
Again, factoring 675 by 5,
27000= 2×2×2×5×5×135
Factoring 135 by 5,
27000= 2×2×2×5×5×5×27
Now, we have to factor 27. We will factor 27 by 3 in the following manner,
27000=2×2×2×5×5×5×3×9
Factoring 9 by 3, we get
27000=2×2×2×5×5×5×3×3×3

27000 = 2^{3} \times 5^{3} \times 3^{3}

27000 = {(2 \times 5 \times 3)}^{3} = 30^{3}

Hence, the cube root of 27000 is 30.

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