Question

find the smallest 297 number by which each of the following number myst be divided to obtains a perfect cube:​

Answer 1

SOLUTION :

Given number :

297

To find :

smallest 297 number by

which each of the following

number must be  divided to

obtains a perfect cube:

Firstly we have to do factorization

$\large{\boxed{\begin{array}{r|1} 3 & 297 \\\\ \cline{2-2} 3 & 99 \\\\ \cline{2-2} 3 & 33 \\\\ \cline{2-2} 11 & 11 \\\\ \cline{2-2} & 1\end{array}}}$

So,

297 = 3 × 3 × 3 × 11

Here,

11 has not 3 pairs so we can

say that 11 is the required number

So,

For making 297 a perfect square we

have to divide 11 by 3 × 3 × 3 × 11

so,

⇒ 3 × 3 × 3 × 11 ÷ 11

⇒ 3  ×  3  ×  3  = 27 is perfect cube.