Question

Find the smallest number by which 2560 must be multiplied so that the product is a
cube.​

Answer 1

Step-by-step explanation:

we try to find by prime factorisation

step by step explaination

\sqrt[3]{2560 }

3

2560

2560=

2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 52×2×2×2×2×2×2×2×2×5

clearly for making cube must be multiply by

5 \times 55×5

= 25=25

both side

2560 \times 25 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 5 \times 5 \times 52560×25=2×2×2×2×2×2×2×2×2×5×5×5

hence,

64060=2560 .

ans. = smallest number is 25

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