Match the given problem to the corresponding simplified radical.(3 points) Put responses in the correct input to answer the question. Select a response 27−−√ 32−−√ 75−−√

Question

answer choices for each one: 4√2, 5√3, 3√3

which option goes to which answer? choose the correct option 100%

Answer 1

To match the problems with their corresponding simplified radicals, we need to simplify each radical:

1. For \( \sqrt{27} \): \[ \sqrt{27} = \sqrt{9 \cdot 3} = \sqrt{9} \cdot \sqrt{3} = 3\sqrt{3} \]

2. For \( \sqrt{32} \): \[ \sqrt{32} = \sqrt{16 \cdot 2} = \sqrt{16} \cdot \sqrt{2} = 4\sqrt{2} \]

3. For \( \sqrt{75} \): \[ \sqrt{75} = \sqrt{25 \cdot 3} = \sqrt{25} \cdot \sqrt{3} = 5\sqrt{3} \]

Now let's match them:

• \( \sqrt{27} \) matches with \( 3\sqrt{3} \)
• \( \sqrt{32} \) matches with \( 4\sqrt{2} \)
• \( \sqrt{75} \) matches with \( 5\sqrt{3} \)

So the correct matches are:

• \( \sqrt{27} \) -> \( 3\sqrt{3} \)
• \( \sqrt{32} \) -> \( 4\sqrt{2} \)
• \( \sqrt{75} \) -> \( 5\sqrt{3} \)

The final answers are:

• \( \sqrt{27} \) → \( 3\sqrt{3} \)
• \( \sqrt{32} \) → \( 4\sqrt{2} \)
• \( \sqrt{75} \) → \( 5\sqrt{3} \)