Question 87805
Given:
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{{{(sqrt(2) - 3)*(sqrt(2) + 3)}}}
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Note that this product is covered by the rule for the product of the sum and difference
of two quantities. This rule is:
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{{{(a - b)*(a + b) = a^2 - b^2}}}
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If you actually do the multiplication of (a - b) times (a + b) you will see why this rule
is true.
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Anyhow, if you let {{{a = sqrt(2)}}} and {{{b = 3}}} then, according to the rule, the product
will be {{{a^2 - b^2}}} or {{{(sqrt(2))^2 - (3)^2}}}.
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But squaring the square root of 2 results in an answer of 2 and squaring 3 results in 9.
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So according to the rule, the answer is:
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{{{(sqrt(2)-3)*(sqrt(2)+3) = (sqrt(2))^2 - (3)^2 = (2 - 9) = -7}}}
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The answer is -7 and notice that the radicals are gone completely.
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