Math, asked by kishanshroof, 1 year ago

find the smallest number by which 137592 to must be multiplied to make it perfect cube find cube root of the product

Answers

Answered by harshbabushah
2
The smallest no is 182

harshbabushah: Welcome
Answered by AnIntrovert
36

To find the smallest number by which 137592 to must be multiplied to make it perfect cube ..

So, first find the prime factorisation of 137592 » 2³ × 3³ × 7² × 13

If we multiply 7 × 13² to 137592 .. it will be a perfect cube ⇒ ( 2 × 3 × 7 × 13 )³

so, the smallest number is 7 × 13² = 1183

and the cube root of product = ³√{(2 × 3 × 7 × 13)³}

= 2 × 3 × 7 × 13 = 546

Therefore the smallest number is 1183 and the cube root of the product is 546.

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