Match the given problem to the corresponding simplified radical. (4 points)

Question

18
√12
√54
√45
L
= 3√5 :: 3√6
# 2√√√3
:: 3√2

Answer 1

To match the given problems to the corresponding simplified radicals, we'll simplify each radical expression.

1. √12:

   • √12 = √(4 * 3) = √4 * √3 = 2√3.

2. √54:

   • √54 = √(9 * 6) = √9 * √6 = 3√6.

3. √45:

   • √45 = √(9 * 5) = √9 * √5 = 3√5.

4. 18:

   • This does not need simplification, but rather we'll compare it appropriately with expressions.

Now, we summarize the results:

• √12 = 2√3
• √54 = 3√6
• √45 = 3√5

Now to match the expressions to the radicals provided in the question, we can see:

• 18 is a whole number and does not correspond to any of the simplified radicals directly.

• 2√3 corresponds to the simplified radical of √12.

• 3√6 corresponds to the simplified radical of √54.

• 3√5 corresponds to the simplified radical of √45.

Thus the matches would be:

• √12 = 2√3
• √54 = 3√6
• √45 = 3√5

The corrected structure would be:

• L = 3√5
• = 3√6 corresponds to √54

• 2√√√3 corresponds to √12

• :: 3√2 does not match any of the radicals provided above.

If there are any specific instructions on how to use these radicals or if further assistance is needed, please let me know!