What is the irrational square root 28−−√

Question

simplified?(1 point)
Responses

27–√
2 start root 7 end root

214−−√
2 start root 14 end root

4–√ ⋅ 7–√
start root 4 end root times start root 7 end root

47–√
4 start root 7 end root

Answer 1

To simplify \( \sqrt{28} \):

1. First, we can factor 28 into its prime factors: \[ 28 = 4 \times 7 \]

2. Now we can rewrite the square root: \[ \sqrt{28} = \sqrt{4 \times 7} \]

3. Using the property of square roots that states \(\sqrt{a \cdot b} = \sqrt{a} \cdot \sqrt{b}\), we can separate the square roots: \[ \sqrt{28} = \sqrt{4} \times \sqrt{7} \]

4. Since \(\sqrt{4} = 2\), we get: \[ \sqrt{28} = 2 \sqrt{7} \]

Thus, the simplified form of \( \sqrt{28} \) is:

\[ 2 \sqrt{7} \]

The correct response is \(2 \sqrt{7}\).