Question

what is √54 simplified

Answer 1

To simplify \(\sqrt{54}\), we first factor 54 into its prime factors:

\[
54 = 9 \times 6 = 3^2 \times 6
\]

Next, we can break it down further since 6 can also be factored:

\[
6 = 2 \times 3
\]

So, the prime factorization of 54 is:

\[
54 = 3^3 \times 2
\]

Now, we can rewrite \(\sqrt{54}\) using its prime factors:

\[
\sqrt{54} = \sqrt{3^3 \times 2}
\]

We can separate the square root of perfect squares:

\[
\sqrt{54} = \sqrt{3^2 \times 3 \times 2} = \sqrt{3^2} \times \sqrt{3 \times 2}
\]

This simplifies to:

\[
\sqrt{54} = 3 \times \sqrt{6} = 3\sqrt{6}
\]

Thus, the simplified form of \(\sqrt{54}\) is:

\[
\boxed{3\sqrt{6}}
\]