Simplify the expression.

square root 45

45 = blank (Type an exact answer, using radicals as needed.)

1 answer

To simplify the expression \(\sqrt{45}\), we first factor \(45\) into its prime factors:

\[ 45 = 9 \times 5 = 3^2 \times 5 \]

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

\[ \sqrt{45} = \sqrt{9 \times 5} = \sqrt{9} \times \sqrt{5} \]

Since \(\sqrt{9} = 3\), we can simplify further:

\[ \sqrt{45} = 3 \times \sqrt{5} \]

Thus, the expression simplifies to:

\[ \sqrt{45} = 3\sqrt{5} \]

So, \(45 = 9 \times 5\). The complete answer is:

\[ \sqrt{45} = 3\sqrt{5} \]