UESTION PART A Consider the radical expression \(6\sqrt{12}-12\sqrt3+\sqrt{100}\) simplify the radical expression QUESTION PART B what is \(9\sqrt{32}-6\sqrt8+\sqrt{25}\) added to the original radical expression from part A?

Answer 1

PART A
First, let's simplify the radical expression \(6\sqrt{12}-12\sqrt3+\sqrt{100}\):

\(6\sqrt{12} = 6 \times 2\sqrt{3} = 12\sqrt{3}\)

\(-12\sqrt{3} = -12\sqrt{3}\)

\(\sqrt{100} = 10\)

Therefore, the simplified radical expression is \(12\sqrt{3} - 12\sqrt{3} + 10 = 10\)

PART B
Now, let's find \(9\sqrt{32}-6\sqrt8+\sqrt{25}\):

\(9\sqrt{32} = 9 \times 4\sqrt{2} = 36\sqrt{2}\)

\(-6\sqrt{8} = -6 \times 2\sqrt{2} = -12\sqrt{2}\)

\(\sqrt{25} = 5\)

Therefore, \(36\sqrt{2} - 12\sqrt{2} + 5 = 24\sqrt{2} + 5\)

When this is added to the simplified radical expression from part A:

\(10 + 24\sqrt{2} + 5 = 15 + 24\sqrt{2}\)

So, the final answer is \(15 + 24\sqrt{2}\)