Question

Find the smallest number which when multiplied with 3600 will make the product cube. Further, find the cube root of the product.

Answer 1

Answer:

$Required\:product = 216000\\and\\\sqrt[3]{216000}=60$

Step-by-step explanation:

Resolving 3600 into prime factors, we get

3600= 2×2×2×2×3×3×5×5

The prime factors 2,3 and 5 doesn't appear in a group of three.

So,3600 is not a perfect cube.

Hence , the smallest number by which it is to be multiplied to make it perfect cube is (2×2×3×5) = 60

product = 3600×60=216000

$\sqrt[3]{3600\times 60}\\=\sqrt[3]{2^{3}\times 2^{3}\times 3^{3}\times 5^{3}}\\=2\times 2\times 3\times 5\\=60$

Therefore,

$Required\:product = 216000\\and\\\sqrt[3]</p><p>{216000}=60$

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Answer 2

Answer:

The smallest number is 60 and the cube root of the product is also 60.

Step-by-step explanation:

To find

1. Smallest number that is to be multiplied with 3600 to get the perfect cube

2. The cube root of the product

Take the LCM for the number 3600

When we take LCM we get 2 x 2x 2x 2x 3x 3x 5x 5 as the sol

=60

Hence 60 smallest number that is multiplied with 3600 to get the perfect cube

The product=3600 x 60

=21600

Cube root of the product  (To find the cube root of 21600 we can also use LCM method.)

$\sqrt[3]{216000}=60$