Question

Simplify √90, leaving your answers in exact form.

Answer 1

To simplify \(\sqrt{90}\), we can start by finding the prime factorization of 90:

\[
90 = 9 \times 10 = 3^2 \times (2 \times 5)
\]

Now we can rewrite \(\sqrt{90}\):

\[
\sqrt{90} = \sqrt{3^2 \times 2 \times 5}
\]

Using the property of square roots that states \(\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}\), we can separate the square root:

\[
\sqrt{90} = \sqrt{3^2} \times \sqrt{2 \times 5}
\]

We know that \(\sqrt{3^2} = 3\):

\[
\sqrt{90} = 3 \times \sqrt{10}
\]

Thus, the simplified form of \(\sqrt{90}\) is:

\[
\sqrt{90} = 3\sqrt{10}
\]

So, the final answer is:

\[
3\sqrt{10}
\]