Match the given problem to the corresponding simplified radical.(3 points)

Question

Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
27−−√
75−−√
32−−√

Answer 1

To simplify the given radicals, we break them down into their prime factors and simplify where possible.

1. √27 can be simplified as follows:

   • 27 = 9 * 3 = 3² * 3
   • Therefore, √27 = √(9 * 3) = √9 * √3 = 3√3.

2. √75 can be simplified as follows:

   • 75 = 25 * 3 = 5² * 3
   • Therefore, √75 = √(25 * 3) = √25 * √3 = 5√3.

3. √32 can be simplified as follows:

   • 32 = 16 * 2 = 4² * 2
   • Therefore, √32 = √(16 * 2) = √16 * √2 = 4√2.

Now, pairing the problems with their corresponding simplified radicals, we have:

• √27 matches with 3√3.
• √75 matches with 5√3.
• √32 matches with 4√2.

Now, you can insert the matched responses where indicated. The corresponding simplified radicals based on the calculations above are:

• √27 → 3√3
• √75 → 5√3
• √32 → 4√2