Answer:
It is the reponse 3
Step-by-step explanation:
because you have to do the square roots first then add them together then multiply by 5
Answer: [tex]5\sqrt{5}[/tex]
Work Shown
[tex]AB+BC\\\\= \sqrt{20}+\sqrt{45}\\\\= \sqrt{4*5}+\sqrt{9*5}\\\\= \sqrt{4}*\sqrt{5}+\sqrt{9}*\sqrt{5}\\\\= 2\sqrt{5}+3\sqrt{5}\\\\= (2+3)\sqrt{5}\\\\= 5\sqrt{5}\\\\[/tex]
Therefore,
[tex]AB+BC= \sqrt{20}+\sqrt{45}= 5\sqrt{5}\\\\[/tex]
You can use a calculator to confirm. The result for both sides should be roughly 11.18034 depending how your calculator rounds the result.
As the steps above show, the idea is to factor out the largest perfect square factor. Then we combine like terms. The last three steps can be thought of as 2x+3x = 5x where [tex]\text{x} = \sqrt{5}[/tex]
