Simplify Radical Expression $(\sqrt{5} + \sqrt{11})(\sqrt{5} - \sqrt{11})$
The given expression is in the form of a difference of squares, which follows the algebraic identity: $(a+b)(a-b) = a^2 - b^2$
In this expression, let $a = \sqrt{5}$ and $b = \sqrt{11}$.
Applying the difference of squares formula:
$(\sqrt{5} + \sqrt{11})(\sqrt{5} - \sqrt{11}) = (\sqrt{5})^2 - (\sqrt{11})^2$Now, we evaluate the squares:
- $(\sqrt{5})^2 = 5$
- $(\sqrt{11})^2 = 11$
Substitute these values back into the equation:
$5 - 11$Performing the subtraction:
$-6$Thus, the expression $(\sqrt{5} + \sqrt{11})(\sqrt{5} - \sqrt{11})$ simplifies to $-6$.
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