Question

plz plz help me !!!
plz plz ​

Answer 1

AnsWer :

• Smallest number be 7.
• Perfect square be 84.

Solution :

We have Number, 1008

$\begin{array}{r | l} 2 & 1008 \\ \cline{2-2} 2 & 504 \\ \cline{2-2} 2 & 252 \\ \cline{2-2} 2 & 126 \\ \cline{2-2} 3 & 63 \\ \cline{2-2} 3 & 21 \\ \cline{2-2} 7 & 7 \\ \cline{2-2} & 1 \end{array}$

Now,

$\tt \bigstar \: 1008 \dashrightarrow 2 \times 2 \times 2 \times 2 \times 3 \times 3 \times 7.$

$\tt \bigstar \: 1008\dashrightarrow {2}^{4} \times {3}^{2} \times 7.$

We notice, When multiple Both side by 7, We get a Perfect square.

$\tt \implies1008 \times 7\dashrightarrow{2}^{4} \times {3}^{2} \times 7 \times 7.$

$\tt \implies7056\dashrightarrow{2}^{4} \times {3}^{2} \times {7 }^{2} .$

Taking Pair,

$\tt \dashrightarrow{2}^{2} \times 3\times 7.$

$\tt \dashrightarrow4 \times 3\times 7.$

$\tt \dashrightarrow84.$

$\rule{200}3$

Let's Verify :

Square of 84.

$\tt \dashrightarrow{84}^{2} = 7056.$

Therefore, the value of smallest number be 7 and Perfect square be 84.