SOLUTION: I'm supposed to express this in simplest radical form. (square root of 2 minus 3)(square root of 2 plus 3) I'm not sure how you are supposed to do that or is it in simplest form

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Question 87805This question is from textbook algebra structure and method
: I'm supposed to express this in simplest radical form.
(square root of 2 minus 3)(square root of 2 plus 3)
I'm not sure how you are supposed to do that or is it in simplest form already?This question is from textbook algebra structure and method

Answer by bucky(2097) About Me  (Show Source):
You can put this solution on YOUR website!
Given:
.
%28sqrt%282%29+-+3%29%2A%28sqrt%282%29+%2B+3%29
.
Note that this product is covered by the rule for the product of the sum and difference
of two quantities. This rule is:
.
%28a+-+b%29%2A%28a+%2B+b%29+=+a%5E2+-+b%5E2
.
If you actually do the multiplication of (a - b) times (a + b) you will see why this rule
is true.
.
Anyhow, if you let a+=+sqrt%282%29 and b+=+3 then, according to the rule, the product
will be a%5E2+-+b%5E2 or %28sqrt%282%29%29%5E2+-+%283%29%5E2.
.
But squaring the square root of 2 results in an answer of 2 and squaring 3 results in 9.
.
So according to the rule, the answer is:
.
%28sqrt%282%29-3%29%2A%28sqrt%282%29%2B3%29+=+%28sqrt%282%29%29%5E2+-+%283%29%5E2+=+%282+-+9%29+=+-7
.
The answer is -7 and notice that the radicals are gone completely.
.