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Simplify the expression (sqrt(5)+2)(sqrt(5)-1)

April 18, 2026Mathematics

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Answer

3 + \sqrt{5}

4 steps

Expand the expression using the distributive property (FOIL method).
$(\sqrt{5}+2)(\sqrt{5}-1) = \sqrt{5} \cdot \sqrt{5} + \sqrt{5} \cdot (-1) + 2 \cdot \sqrt{5} + 2 \cdot (-1)$
Perform the multiplications.
$= 5 - \sqrt{5} + 2\sqrt{5} - 2$
Group the like terms (constants and terms with $\sqrt{5}$ ).
$= (5 - 2) + (-\sqrt{5} + 2\sqrt{5})$
Simplify the grouped terms.
$= 3 + \sqrt{5}$
The answer in surd form is:
$3 + \sqrt{5}$

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