Question

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Explanation:

Step1: Simplify $\sqrt{25}$

We know that $\sqrt{25} = 5$ because $5\times5 = 25$. So the first blank (coefficient of $\sqrt{5}$ from $\sqrt{25}\cdot\sqrt{5}$) is 5.

Step2: Simplify $\sqrt{16}$

We know that $\sqrt{16}=4$ because $4\times4 = 16$. So the second blank (coefficient of $\sqrt{5}$ from $\sqrt{16}\cdot\sqrt{5}$) is 4.

Step3: Combine like terms

Now we have $5\sqrt{5}+4\sqrt{5}$. Since the terms have the same radical part, we can add the coefficients: $(5 + 4)\sqrt{5}=9\sqrt{5}$.

Answer:

First blank: $5$, Second blank: $4$, Final result: $9\sqrt{5}$