Final answer:
The expression √5(3√18 - 2√8) simplifies to 10√5 after breaking down the square roots, combining like terms, and multiplying through by √5.
Step-by-step explanation:
To solve the expression √5(3√18 - 2√8), we first need to simplify the square roots within the brackets. We can break them down into prime factors: √18 = √(9×2) = 3√2 and √8 = √(4×2) = 2√2. After simplification, the expression inside the brackets becomes 3×3√2 - 2×2√2, which simplifies to 9√2 - 4√2.
Now, combine the like terms: 9√2 - 4√2 equals 5√2. Finally, multiply this by √5 from outside the brackets to get our final answer: √5 × 5√2, which equals 5×2√5 after combining the radicals (since √5 × √2 = √10). Therefore, the final simplified form is 10√5.