find the cube root of 27744,-2197, 9261,39304,74088
Answers
Step-by-step explanation:
(i)
On factorising 64 into prime factors, we get:
64=2×2×2×2×2×2
On grouping the factors in triples of equal factors, we get:
64={2×2×2}×{2×2×2}
It is evident that the prime factors of 64 can be grouped into triples of equal factors and no factor is left over. Therefore, 64 is a perfect cube. This implies that -64 is also a perfect cube.
Now, collect one factor from each triplet and multiply, we get:
2×2=4
This implies that 64 is a cube of 4.
Thus, -64 is the cube of -4.
(ii)
On factorising 1056 into prime factors, we get:
1056=2×2×2×2×2×3×11
On grouping the factors in triples of equal factors, we get:
1056={2×2×2}×2×2×3×11
It is evident that the prime factors of 1056 cannot be grouped into triples of equal factors such that no factor is left over. Therefore, 1056 is not a perfect cube. This implies that -1056 is not a perfect cube as well.
(iii)
On factorising 2197 into prime factors, we get:
2197=13×13×13
On grouping the factors in triples of equal factors, we get:
2197={13×13×13}
It is evident that the prime factors of 2197 can be grouped into triples of equal factors