Question

fi find the smallest number by which 50094 must be divided so that it become a perfect square​

Answer 1

Answer:

• The smallest number by which 50094 must be divided so that it become a perfect square is 1089

Given:

• 50094

To find:

• find the smallest number by which 50094 must be divided so that it will become a perfect square?

Let's do this by prime factorization method :

$\Large{ \begin{array}{c|c} \tt 2 & \sf{50094 } \\ \cline{1-2} \tt 3 & \sf { 25047} \\ \cline{1-2}\tt 3 & \sf{8349 } \\ \cline{1-2} \tt 11 & \sf{2783 } \\ \cline{1-2} \tt 11& \sf{ 253}\\ \cline{1-2} & \sf{ 23} \end{array}}$

Factors of 50094 = 2 × 3 × 3 × 11 × 11 × 23

Now,

The pairs are :- 2 × ( 3 × 3 ) × ( 11 × 11 ) × 23

√50094 = √2 × 3 × 11 × 23

Thus, 2 and 23 are not in any pair.

• 2 × 23 = 46.

Hence, 50094 must be divided by 46 so that it will become a perfect square.

Check :-

$\bf \dfrac{50094}{46}$ = 1089

Here, 1089 is a perfect square.

• Square root of √1089 = 33