Simplify ( square root of 5+4)( square root of 5-2)

$(\sqrt{5} + 4) (\sqrt{5} - 2)$

Step 1

Expand $(\sqrt{5} + 4) (\sqrt{5} - 2)$ using the FOIL Method.

Apply the distributive property.

$\sqrt{5} (\sqrt{5} - 2) + 4 (\sqrt{5} - 2)$

Apply the distributive property.

$\sqrt{5} \sqrt{5} + \sqrt{5} \cdot - 2 + 4 (\sqrt{5} - 2)$

Apply the distributive property.

$\sqrt{5} \sqrt{5} + \sqrt{5} \cdot - 2 + 4 \sqrt{5} + 4 \cdot - 2$

Step 2

Simplify and combine like terms.

Simplify each term.

Combine using the product rule for radicals.

$\sqrt{5 \cdot 5} + \sqrt{5} \cdot - 2 + 4 \sqrt{5} + 4 \cdot - 2$

Multiply $5$ by $5$ .

$\sqrt{25} + \sqrt{5} \cdot - 2 + 4 \sqrt{5} + 4 \cdot - 2$

Rewrite $25$ as $5^{2}$ .

$\sqrt{5^{2}} + \sqrt{5} \cdot - 2 + 4 \sqrt{5} + 4 \cdot - 2$

Pull terms out from under the radical, assuming positive real numbers.

$5 + \sqrt{5} \cdot - 2 + 4 \sqrt{5} + 4 \cdot - 2$

Move $- 2$ to the left of $\sqrt{5}$ .

$5 - 2 \cdot \sqrt{5} + 4 \sqrt{5} + 4 \cdot - 2$

Multiply $4$ by $- 2$ .

$5 - 2 \sqrt{5} + 4 \sqrt{5} - 8$

Subtract $8$ from $5$ .

$- 3 - 2 \sqrt{5} + 4 \sqrt{5}$

Add $- 2 \sqrt{5}$ and $4 \sqrt{5}$ .

$- 3 + 2 \sqrt{5}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$- 3 + 2 \sqrt{5}$

Decimal Form:

$1.47213595 \dots$