Given:
The expression is
[tex](7-\sqrt{7})(-6+\sqrt{7})[/tex]
To find:
The product of the radical expression.
Solution:
We have,
[tex](7-\sqrt{7})(-6+\sqrt{7})[/tex]
Using distributive propertry, we get
[tex]=(7)(-6)+(7)(\sqrt{7})+(-\sqrt{7})(-6)+(-\sqrt{7})(\sqrt{7})[/tex]
[tex]=-42+7\sqrt{7}+6\sqrt{7}-7[/tex]
On combining like term, we get
[tex]=(-42+7)+(7\sqrt{7}+6\sqrt{7})[/tex]
[tex]=-49+13\sqrt{7}[/tex]
Therefore, the product of the given radical expression is [tex]-49+13\sqrt{7}[/tex].
