Question

(9 - square root 3)(5 + square root 15)

Answer 1

To simplify the expression \((9 - \sqrt{3})(5 + \sqrt{15})\), we can use the distributive property (also known as the FOIL method for binomials).

Let's calculate it step-by-step:

1. **First terms**:
\[
9 \cdot 5 = 45
\]

2. **Outer terms**:
\[
9 \cdot \sqrt{15} = 9\sqrt{15}
\]

3. **Inner terms**:
\[
-\sqrt{3} \cdot 5 = -5\sqrt{3}
\]

4. **Last terms**:
\[
-\sqrt{3} \cdot \sqrt{15} = -\sqrt{45}
\]
We can simplify \(\sqrt{45}\) as follows:
\[
\sqrt{45} = \sqrt{9 \cdot 5} = \sqrt{9} \cdot \sqrt{5} = 3\sqrt{5}
\]

Now we can combine all these results:
\[
(9 - \sqrt{3})(5 + \sqrt{15}) = 45 + 9\sqrt{15} - 5\sqrt{3} - 3\sqrt{5}
\]

So, the simplified expression is:
\[
45 + 9\sqrt{15} - 5\sqrt{3} - 3\sqrt{5}
\]

That's the final result.