Finite Math Examples

$(5 \sqrt{7} - 3 \sqrt{3}) (\sqrt{7 + \sqrt{3}})$

Step 1

Apply the distributive property.

$5 \sqrt{7} \sqrt{7 + \sqrt{3}} - 3 \sqrt{3} \sqrt{7 + \sqrt{3}}$

Step 2

Combine using the product rule for radicals.

$5 \sqrt{(7 + \sqrt{3}) \cdot 7} - 3 \sqrt{3} \sqrt{7 + \sqrt{3}}$

Step 3

Combine using the product rule for radicals.

$5 \sqrt{(7 + \sqrt{3}) \cdot 7} - 3 \sqrt{(7 + \sqrt{3}) \cdot 3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$5 \sqrt{(7 + \sqrt{3}) \cdot 7} - 3 \sqrt{(7 + \sqrt{3}) \cdot 3}$

Decimal Form:

$23.73638028 \dots$