Simplify √90, leaving your answers in exact form.

1 answer

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:

\[ 3\sqrt{10} \]