Simplify (2+ square root of 5)(5- square root of 7)

$(2 + \sqrt{5}) (5 - \sqrt{7})$

Step 1

Expand $(2 + \sqrt{5}) (5 - \sqrt{7})$ using the FOIL Method.

Apply the distributive property.

$2 (5 - \sqrt{7}) + \sqrt{5} (5 - \sqrt{7})$

Apply the distributive property.

$2 \cdot 5 + 2 (- \sqrt{7}) + \sqrt{5} (5 - \sqrt{7})$

Apply the distributive property.

$2 \cdot 5 + 2 (- \sqrt{7}) + \sqrt{5} \cdot 5 + \sqrt{5} (- \sqrt{7})$

Step 2

Simplify each term.

Multiply $2$ by $5$ .

$10 + 2 (- \sqrt{7}) + \sqrt{5} \cdot 5 + \sqrt{5} (- \sqrt{7})$

Multiply $- 1$ by $2$ .

$10 - 2 \sqrt{7} + \sqrt{5} \cdot 5 + \sqrt{5} (- \sqrt{7})$

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

$10 - 2 \sqrt{7} + 5 \cdot \sqrt{5} + \sqrt{5} (- \sqrt{7})$

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

Combine using the product rule for radicals.

$10 - 2 \sqrt{7} + 5 \sqrt{5} - \sqrt{5 \cdot 7}$

Multiply $5$ by $7$ .

$10 - 2 \sqrt{7} + 5 \sqrt{5} - \sqrt{35}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$10 - 2 \sqrt{7} + 5 \sqrt{5} - \sqrt{35}$

Decimal Form:

$9.97275748 \dots$