Match the given problem to the corresponding simplified radical (points) sqrt(54); sqrt(12); sqrt(18); sqrt(45); 2sqrt(3); 3sqrt(2); 3sqrt(5) * 3sqrt(6)

Answer 1

Let's simplify each of the radical expressions provided:

1. √54:

   • √54 = √(9 * 6) = √9 * √6 = 3√6.

2. √12:

   • √12 = √(4 * 3) = √4 * √3 = 2√3.

3. √18:

   • √18 = √(9 * 2) = √9 * √2 = 3√2.

4. √45:

   • √45 = √(9 * 5) = √9 * √5 = 3√5.

5. 2√3:

   • This is already in simplified form.

6. 3√2:

   • This is already in simplified form.

7. 3√5 * 3√6:

   • (3√5)(3√6) = 9√(5 * 6) = 9√30.

Now, let’s match the given problems to their corresponding simplified radicals:

• √54 = 3√6
• √12 = 2√3
• √18 = 3√2
• √45 = 3√5
• 2√3 = 2√3
• 3√2 = 3√2
• 3√5 * 3√6 = 9√30 (not listed in your options)

So the matches are:

• √54 → 3√6
• √12 → 2√3
• √18 → 3√2
• √45 → 3√5
• 2√3 → 2√3
• 3√2 → 3√2
• 3√5 * 3√6 → 9√30 (not listed, but calculated).