9. What is the smallest number by which 1600 must be divided so that the quotient is a perfect cube? 10. Find the smallest number by which 8788 must be divided so that the quotient is a perfect cube.
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Answer:
9.Firstly we need to factorize the number 1600
After factorization we get,
⇒1600= 2∗2∗2
∗ 2∗2∗2
∗ 5∗5
We need to group the expanded numbers in a group of three since it has to be a perfect cube.
The number 5 does not form a triplet. It contains only two 5 ′
s. Hence the number 5×5=25 has to be divided so that the quotient becomes a perfect cube.
10.Prime factorising 8788, we get,
8788=2×2×13×13×13
=22
×133
.
We know, a perfect cube has multiples of 3 as powers of prime factors.
Here, number of 2’s is 2 and number of 13’s is 3.
So we need to divide 22 from the factorization to make 8788 a perfect cube.
Hence, the smallest number by which 8788 must be divided to obtain a perfect cube is 22
=4.
Plz. mark my answer as the brainliest. I really need it.
Answer:
9.Firstly we need to factorize the number 1600
After factorization we get,
⇒1600= 2∗2∗2
∗ 2∗2∗2
∗ 5∗5
We need to group the expanded numbers in a group of three since it has to be a perfect cube.
The number 5 does not form a triplet. It contains only two 5 ′
s. Hence the number 5×5=25 has to be divided so that the quotient becomes a perfect cube.
10.Prime factorising 8788, we get,
8788=2×2×13×13×13
=22
×133
.
We know, a perfect cube has multiples of 3 as powers of prime factors.
Here, number of 2’s is 2 and number of 13’s is 3.
So we need to divide 22 from the factorization to make 8788 a perfect cube.
Hence, the smallest number by which 8788 must be divided to obtain a perfect cube is 22
=4.
Plz. mark my answer as the brainliest. I really need it.