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Simplify \newline(5+3)(5−3)22\frac{(5+\sqrt{3})(5-\sqrt{3})}{\sqrt{22}}\newlineGive your answer in its simplest form.

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Full solution

Q. Simplify \newline(5+3)(5−3)22\frac{(5+\sqrt{3})(5-\sqrt{3})}{\sqrt{22}}\newlineGive your answer in its simplest form.
  1. Apply Difference of Squares: Apply the difference of squares formula to the numerator (5+3)(5−3)(5+\sqrt{3})(5-\sqrt{3}).\newline(5+\sqrt{3})(5-\sqrt{3}) = 5^2 - (\sqrt{3})^2\(\newline= 25 - 3\newline= 22\)
  2. Write Simplified Expression: Now that we have simplified the numerator, let's write down the expression with the simplified numerator. (5+3)(5−3)22=2222\frac{(5+\sqrt{3})(5-\sqrt{3})}{\sqrt{22}} = \frac{22}{\sqrt{22}}
  3. Divide to Simplify: Simplify the expression by dividing 2222 by 22\sqrt{22}. 2222=22\frac{22}{\sqrt{22}} = \sqrt{22}

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