Q

# Find the smallest number by which each of the following numbers must be multiplied to obtain a perfect cube.

Q.2 Find the smallest number by which each of the following numbers must be multiplied to obtain a perfect cube.

(i) 243

(ii) 256

(iii) 72

(iv) 675

(v) 100

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This can be found by knowing about the prime factors of the number.

(i) 243 :     $3\times3\times3\times3\times3$.

So it must be multiplied by 3.

(ii) 256 :    $2\times2\times2\times2\times2\times2\times2\times2$

So the given number must be multiplied by 2 to make it a perfect cube.

(iii) 72 :    $2\times2\times2\times3\times3$

So 72 must be multiplied by 3 to make it a perfect cube.

(iv) 675 :  $3\times3\times3\times5\times5$

So it should be multiplied by 5.

(v) 100 :   $2\times2\times5\times5$

So it should be multiplied by 10.

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