Question

select the correct answer.

which expression is in its simplest form?

\\(\bigcirc\\ \sqrt{21}\\)

\\(\bigcirc\\ 3\sqrt{24}\\)

\\(\bigcirc\\ 7\sqrt{8}\\)

\\(\bigcirc\\ 9\sqrt{9}\\)

Explanation:

⚡ Using what you learned: simplifying radical expressions

Step 1: Analyze \(\sqrt{21}\)

The prime factorization of \(21\) is:

$$ 21 = 3 \times 7 $$

Since there are no perfect square factors other than \(1\), \(\sqrt{21}\) cannot be simplified further.

Step 2: Analyze \(3\sqrt{24}\)

The prime factorization of \(24\) is:

$$ 24 = 4 \times 6 = 2^2 \times 6 $$

Since \(4\) is a perfect square factor:

$$ 3\sqrt{24} = 3\sqrt{4 \times 6} = 3 \times 2\sqrt{6} = 6\sqrt{6} $$

This expression is not in its simplest form.

Step 3: Analyze \(7\sqrt{8}\)

The prime factorization of \(8\) is:

$$ 8 = 4 \times 2 = 2^2 \times 2 $$

Since \(4\) is a perfect square factor:

$$ 7\sqrt{8} = 7\sqrt{4 \times 2} = 7 \times 2\sqrt{2} = 14\sqrt{2} $$

This expression is not in its simplest form.

Step 4: Analyze \(9\sqrt{9}\)

Since \(9\) is a perfect square:

$$ 9\sqrt{9} = 9 \times 3 = 27 $$

This expression is not in its simplest form.

Answer:

\(\sqrt{21}\)