Final answer:
To simplify the expression 3√18 + 2√50, we simplify each radical and then combine the terms. The simplified expression is 5√2, corresponding to option a) 15√2.
Step-by-step explanation:
To simplify the expression 3√18 + 2√50, we need to simplify each radical separately and then combine the simplified terms.
Start with the first radical √18. To simplify, we can break down 18 into its prime factorization: 18 = 2 x 3 x 3. We can simplify the square root of 9 (which is 3) outside of the radical: √18 = √(2 x 3 x 3) = 3√2.
Next, simplify the second radical √50. Break down 50 into its prime factorization: 50 = 2 x 5 x 5. Simplify the square root of 25 (which is 5) outside of the radical: √50 = √(2 x 5 x 5) = 5√2.
Now we can combine the simplified terms: 3√2 + 2√2 = (3 + 2)√2 = 5√2.
Therefore, the simplified expression is 5√2, which corresponds to option a) 15√2.