The tangent secant theorem says
PR × PS = PQ²
4 × (4+5) = PQ²
36 = PQ²
PQ=6
Answer: 6
12500 cause 5000 goes into 12500 twice and it would be 24$ for 10000 sqft and then another 6 so 30$ cause 2500 is half of 5000
Short answer: 2 * sqrt(13)
Remark
There are a number of ways to look at this. I'll pick the easiest.
Step one
Factor 52 until there are no more prime factors to be used.
52 = 2 * 26
52 = 2 * 2 * 13. That's as far as you can go.
Rule
For every 2 equal prime factors, 1 of them can be taken out side of the root sign. The other one disappears.
sqrt(52) = sqrt(2*2* 13) = 2*sqrt(13)
Answer 2sqrt(13) <<<< answer
