Final answer:
To simplify 5 + √18 / √2 + 1 into the form A + B√C, we reduce √18 to 3√2, divide by √2, and then add the result to 5 + 1, obtaining A = 9, B = 0, and C = 1.
Step-by-step explanation:
The student asked to express the expression 5 + √18 / √2 + 1 in the form A + B√C, where B and C are integers. To do this, first, simplify √18 by identifying it as 3√2 since 18 is 9*2 and √9 is 3. Then, divide 3√2 by √2; the √2 terms will cancel out, leaving us with 3. Add this to 5 and 1 to get the final simplified expression 9. Therefore, if we express it in the form A + B√C, where B and C are integers, we get A = 9, B = 0, and C = 1 (since any number multiplied by 0 will yield 0).