+2 votes
by kratos

What is the smallest number by which the following numbers must be multiplied, so that the products are perfect cubes?

(i) 675

(ii) 1323

(iii) 2560

(iv) 7803

1 Answer

+6 votes
by kratos
 
Best answer

(i) 675

675 = 3 × 3 × 3 × 5 × 5

= 33 × 52

∴To make a perfect cube we need to multiply the product by 5.

(ii) 1323

1323 = 3 × 3 × 3 × 7 × 7

= 33 × 72

∴To make a perfect cube we need to multiply the product by 7.

(iii) 2560

2560 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 5

= 23 × 23 × 23 × 5

∴To make a perfect cube we need to multiply the product by 5 × 5 = 25.

(iv) 7803

7803 = 3 × 3 × 3 × 17 × 17

= 33 × 172

∴To make a perfect cube we need to multiply the product by 17.

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