Answer:
[tex]54-\sqrt{2} [/tex]
Step-by-step explanation:
We have been given a radical expression [tex](7-\sqrt{2}) (8+\sqrt{2)}[/tex] and we are asked to find the product of our given expression.
Upon using FOIL method we will get,
[tex]7(8+\sqrt{2})-\sqrt{2} (8+\sqrt{2} )[/tex]
Now let us simplify our radical expression.
[tex](56+7\sqrt{2})-(8\sqrt{2} +\sqrt{4} )[/tex]
[tex]56+7\sqrt{2}-8\sqrt{2} -\sqrt{4} [/tex]
[tex]56+7\sqrt{2}-8\sqrt{2} -2 [/tex]
Now let us combine like terms.
[tex](56-2)+(7-8)\sqrt{2} [/tex]
[tex](54)+(-1)\sqrt{2} [/tex]
[tex]54-\sqrt{2} [/tex]
Therefore, product of our radical expression is [tex]54-\sqrt{2} [/tex].
