Question

For each of the following number, find
the smallest number by which it should
be divided to make it a perfect square.
Also, find the square root.
b. 1008
a. 1458​

Answer 1

Answer:-

• a) 1008 should be divided by 7 to make it a perfect square.

• b) 1458 should be divided by 2 to make it a perfect cube.

Explanation:-

Given Numbers:-

• a) 1008.
• b) 1458.

To Find:-

• The number from which the above number should be divided to make it a perfect square.

Now,

Let us first find out the factors of 1008,

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

So we get,

$\\ \bf\mapsto 1008 = \underbrace{2 \times 2} \times \underbrace{2 \times 2} \times \underbrace{3 \times 3} \times 7.$

Clearly we can see that only 7 Is not making pair as there is only one 7.

Therefore 1008 should be divided by 7 to make it a perfect square.

Similarly,

Let us find out the factors of 1458,

$\thicklines\begin{array}{r|l} 2 & 1458\\ \cline{1-2} 3 & 729\\ \cline{1-2} 3 & 243\\ \cline{1-2} 3 & 81\\ \cline{1-2} 3 & 27\\ \cline{1-2} 3 & 9\\ \cline{1-2} 3 & 3\\ \cline{1-2} & 1\end{array}$

So we get,

$\\ \bf\mapsto1458 =2 \times \underbrace{3 \times 3} \times \underbrace{3 \times 3} \times \underbrace{3 \times 3} .$

Clearly we can see that only 2 is not making pair as their is only one 2.

Therefore 1458 should be divided by 2 to make it a perfect square.