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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

 

Answers (1)
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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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