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

April 18, 2026Mathematics

ScanSolve AI Answer

April 18, 2026

Answer

$3 + \sqrt{5}$

Step 1: Expand the expression using the distributive property (FOIL method). $(\sqrt{5}+2)(\sqrt{5}-1) = \sqrt{5} \cdot \sqrt{5} + \sqrt{5} \cdot (-1) + 2 \cdot \sqrt{5} + 2 \cdot (-1)$

Step 2: Perform the multiplications. $= 5 - \sqrt{5} + 2\sqrt{5} - 2$

Step 3: Group the like terms (constants and terms with $\sqrt{5}$ ). $= (5 - 2) + (-\sqrt{5} + 2\sqrt{5})$

Step 4: Simplify the grouped terms. $= 3 + \sqrt{5}$

The answer in surd form is: $\boxed{3 + \sqrt{5}}$ Send me the next one 📸

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Quick Answer

Expand the expression using the distributive property (FOIL method). (sqrt(5)+2)(sqrt(5)-1) = sqrt(5) · sqrt(5) + sqrt(5) · (-1) + 2 · sqrt(5) + 2 · (-1) Step 2: Perform the multiplications.

Asked on April 18, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

ScanSolve AI AnswerAnswered on April 18, 2026

Step 1: Expand the expression using the distributive property (FOIL method). (sqrt(5)+2)(sqrt(5)-1) = sqrt(5) · sqrt(5) + sqrt(5) · (-1) + 2 · sqrt(5) + 2 · (-1) Step 2: Perform the multiplications. = 5 - sqrt(5) + 2sqrt(5) - 2 Step 3: Group the like terms (constants and terms with sqrt(5)). = (5 - 2) + (-sqrt(5) + 2sqrt(5)) Step 4: Simplify the grouped terms. = 3 + sqrt(5) The answer in surd form is: 3 + sqrt(5) Send me the next one 📸