Final answer:
The sum of the radicals √2 and √8 is 3√2 after simplifying √8 to 2√2 and then combining like terms.
Step-by-step explanation:
The student asked for the sum of each pair of radicals, specifically √2 and √8. To find the sum, we first look for any opportunities to simplify the radicals. Given that √8 can be simplified to 2√2 (since 8 is 4×2 and √4 is 2), we then add the simplified forms together.
Hence, √2 + 2√2 = √2 + 2√2 = 3√2. Therefore, the sum of the radicals √2 and √8 is 3√2.