What is the irrational square root 28−−√

Question

simplified?(1 point)
Responses

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

27–√
2 start root 7 end root

47–√
4 start root 7 end root

214−−√
2 start root 14 end root

Answer 1

To simplify \(\sqrt{28}\), we can factor 28 into its prime factors:

\[ 28 = 4 \times 7 \]

Now we can use the property of square roots that says \(\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}\):

\[ \sqrt{28} = \sqrt{4 \times 7} = \sqrt{4} \times \sqrt{7} \]

Since \(\sqrt{4} = 2\), we have:

\[ \sqrt{28} = 2 \sqrt{7} \]

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

\[ 2 \sqrt{7} \]

The correct response is: 2 start root 7 end root.