Answer:
the smallest number = 11
Step-by-step explanation:
To find the smallest number by which 539 should be multiplied to become a perfect square, we have to understand that the condition for any perfect square number is:
[tex]\boxed{\texttt{the power of all of its prime factors have to be even numbers}}[/tex]
First, we factorize 539:
[tex]539=7^2\times11[/tex]
We can see that 7 has an even power (to power of 2) but 11 has an odd power (to the power of 1). Therefore, we have have multiply it with 11, so that the factor 11 also has an even power.
[tex]\begin{aligned}(7^2\times11)\times11&=539\times11\\7^2\times11^2&=5929\\7^2\times11^2&=\sqrt{77} \end{aligned}[/tex]