Question

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

Answer 1

as u can see, after prime factorisation, there is no pair for 13 , 7 , 7 . So the number should be multiplied by 169✖7= 1183 to make it a perfect cube

Answer 2

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.