Simplify the Radical Expression ( square root of 5-7)( square root of 5-7)

$(\sqrt{5} - 7) (\sqrt{5} - 7)$

Expand $(\sqrt{5} - 7) (\sqrt{5} - 7)$ using the FOIL Method.

Apply the distributive property.

$\sqrt{5} (\sqrt{5} - 7) - 7 (\sqrt{5} - 7)$

Apply the distributive property.

$\sqrt{5} \sqrt{5} + \sqrt{5} \cdot - 7 - 7 (\sqrt{5} - 7)$

Apply the distributive property.

$\sqrt{5} \sqrt{5} + \sqrt{5} \cdot - 7 - 7 \sqrt{5} - 7 \cdot - 7$

Simplify and combine like terms.

Simplify each term.

Combine using the product rule for radicals.

$\sqrt{5 \cdot 5} + \sqrt{5} \cdot - 7 - 7 \sqrt{5} - 7 \cdot - 7$

Multiply $5$ by $5$ .

$\sqrt{25} + \sqrt{5} \cdot - 7 - 7 \sqrt{5} - 7 \cdot - 7$

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

$\sqrt{5^{2}} + \sqrt{5} \cdot - 7 - 7 \sqrt{5} - 7 \cdot - 7$

Pull terms out from under the radical.

$| 5 | + \sqrt{5} \cdot - 7 - 7 \sqrt{5} - 7 \cdot - 7$

The absolute value is the distance between a number and zero. The distance between $0$ and $5$ is $5$ .

$5 + \sqrt{5} \cdot - 7 - 7 \sqrt{5} - 7 \cdot - 7$

Move $- 7$ to the left of $\sqrt{5}$ .

$5 - 7 \cdot \sqrt{5} - 7 \sqrt{5} - 7 \cdot - 7$

Multiply $- 7$ by $- 7$ .

$5 - 7 \sqrt{5} - 7 \sqrt{5} + 49$

Add $5$ and $49$ .

$54 - 7 \sqrt{5} - 7 \sqrt{5}$

Subtract $7 \sqrt{5}$ from $- 7 \sqrt{5}$ .

$54 - 14 \sqrt{5}$

The result can be shown in multiple forms.

Exact Form:

$54 - 14 \sqrt{5}$

Decimal Form:

$22.69504831 \dots$