Question

What is the irrational square root 28−−√ simplified?(1 point)
Responses

214−−√
2 start root 14 end root

47–√
4 start root 7 end root

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

27–√

Answer 1

To simplify the square root of 28, we can factor it into its prime factors:

\[
28 = 4 \times 7
\]

Now, we can use the property of square roots that states \(\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}\). Thus, we can write:

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

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

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

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

\[
2\sqrt{7}
\]

So the correct response is:

**2\(\sqrt{14}\)**