Simplify the expression.

Question

square root 45

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

Answer 1

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:

$$\sqrt{45}=3\sqrt{5}$$