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Simplify (sqrt(7)+2)(sqrt(7)-1)

April 18, 2026Mathematics

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Answer

5 + \sqrt{7}

4 steps

Expand the expression using the distributive property (FOIL method).
$(\sqrt{7}+2)(\sqrt{7}-1) = \sqrt{7} \cdot \sqrt{7} + \sqrt{7} \cdot (-1) + 2 \cdot \sqrt{7} + 2 \cdot (-1)$
Perform the multiplications.
$= 7 - \sqrt{7} + 2\sqrt{7} - 2$
Group the like terms (constants and terms with $\sqrt{7}$ ).
$= (7 - 2) + (-\sqrt{7} + 2\sqrt{7})$
Simplify the grouped terms.
$= 5 + \sqrt{7}$
The answer in surd form is:
$5 + \sqrt{7}$

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