100 - Find the smallest number by which the given number must be multiplied to obtain a perfect cube?
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Answered by
2
Hey there!
100 = 2 * 50
= 2 * 2 * 25
= 2² * 5²
So, To make the given number a perfect cube, You need to have one more 2 , 5 as part of its prime factorization.
2 * 5 = 10
The least number by which 100 be multiplied to get a perfect cube is 10 .
Multiplying 100 by 10 , you obtain 1000
whose prime factorization has triplets of 2 & 5
1000 = 2³ * 5³
Therefore, The smallest number by which the given number should be multiplied to obtain a perfect cube is 10
100 = 2 * 50
= 2 * 2 * 25
= 2² * 5²
So, To make the given number a perfect cube, You need to have one more 2 , 5 as part of its prime factorization.
2 * 5 = 10
The least number by which 100 be multiplied to get a perfect cube is 10 .
Multiplying 100 by 10 , you obtain 1000
whose prime factorization has triplets of 2 & 5
1000 = 2³ * 5³
Therefore, The smallest number by which the given number should be multiplied to obtain a perfect cube is 10
Answered by
6
100 = 2×25×2
100 = 2×5×5×2
100 = 2^2×5^2
to get cube we need one 2 and one 5
2 × 5 = 10
multiply 100 with 10 we get ;
10 × 100 = 1000
2×5×25×4 = 1000
2×5×5×5×2×2 = 1000
2^3×5^3 = 1000
therefore...the smallest number by which the given number must be multiplied to obtain a perfect cube is 10
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100 = 2×5×5×2
100 = 2^2×5^2
to get cube we need one 2 and one 5
2 × 5 = 10
multiply 100 with 10 we get ;
10 × 100 = 1000
2×5×25×4 = 1000
2×5×5×5×2×2 = 1000
2^3×5^3 = 1000
therefore...the smallest number by which the given number must be multiplied to obtain a perfect cube is 10
hope it helps you. . . . . follow me. . . . . . mark as a brainlist. . . . .
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