Question

2
The smallest number should 7803 be multiplied with so that the product becom
a perfect cube is
a) 3
b) 17
c) 9
d) 289
​

Answer 1

$\large{ \bold{7803 = 3 \times 2601}} \\ \\ \large{ \bold{7803 = 3 \times 3 \times 867}} \\ \\ \large{ \bold{7803 = 3 \times 3 \times 3 \times 289}} \\ \\ \large{ \bold{7803 = 3 \times 3 \times 3 \times 17 \times 17}} \\ \\ \large{ \bold{7803 = {3}^{3} \times {17}^{2} }} \\ \\ \large{ \bold{7803 \times 17 = {3}^{3} \times {17}^{3} }} \\ \\ \large{ \bold{ \sqrt[3]{7803 \times 17} = \sqrt[3]{ {3}^{3} \times {17}^{3} } } } \\ \\ \large{ \bold{ \sqrt[3]{7803 \times 17} = 17 \times 3 = 51}} \\ \\ \large{ \bold{therefore \: the \: multiplied \: number \: is \: 17}}$

$\large{ \bold{correct \: option \: is \: (b)}} \\ \\ \large{ \bold{hope \: it \: helps}}$