To solve the expression $\frac{\sqrt{45}}{3}$, follow these steps:

Step 1: Simplify the square root

Start by simplifying $\sqrt{45}$. We can break down 45 into its prime factors:

$45 = 9 \times 5$

Since $\sqrt{9} = 3$, we can rewrite $\sqrt{45}$ as:

$\sqrt{45} = \sqrt{9 \times 5} = \sqrt{9} \times \sqrt{5} = 3\sqrt{5}$

Step 2: Divide by 3

Now substitute $3\sqrt{5}$ back into the original expression $\frac{\sqrt{45}}{3}$:

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

The 3s cancel out:

$= \sqrt{5}$

Final Answer:

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

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Would you like further details or have any other questions?

Related Questions:

1. How do you simplify other square roots with prime factors?
2. What is the general process for simplifying expressions with square roots?
3. How do you divide numbers with square roots?
4. How would you calculate a similar expression, like $\frac{\sqrt{72}}{6}$?
5. What is the relationship between square roots and prime factorization?

Tip:

When simplifying square roots, always try to factor the number under the square root into perfect squares, as this will make the simplification process easier.