Question

(8 + square root 11)(7 - square root 3)

Answer 1

To simplify the expression \((8 + \sqrt{11})(7 - \sqrt{3})\), we can use the distributive property (also known as the FOIL method for binomials).

We will calculate this step by step:

1. **First:** Multiply the first terms.
\[
8 \times 7 = 56
\]

2. **Outer:** Multiply the outer terms.
\[
8 \times (-\sqrt{3}) = -8\sqrt{3}
\]

3. **Inner:** Multiply the inner terms.
\[
\sqrt{11} \times 7 = 7\sqrt{11}
\]

4. **Last:** Multiply the last terms.
\[
\sqrt{11} \times (-\sqrt{3}) = -\sqrt{33}
\]

Now, combine all of these results:
\[
56 - 8\sqrt{3} + 7\sqrt{11} - \sqrt{33}
\]

Thus, the simplified form of the expression \((8 + \sqrt{11})(7 - \sqrt{3})\) is:
\[
56 + 7\sqrt{11} - 8\sqrt{3} - \sqrt{33}
\]