Evaluate square root of 3( square root of 7- square root of 5)

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

Step 1

Apply the distributive property.

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

Step 2

Combine using the product rule for radicals.

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

Step 3

Multiply $\sqrt{3} (- \sqrt{5})$ .

Combine using the product rule for radicals.

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

Multiply $3$ by $5$ .

$\sqrt{3 \cdot 7} - \sqrt{15}$

Step 4

Multiply $3$ by $7$ .

$\sqrt{21} - \sqrt{15}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\sqrt{21} - \sqrt{15}$

Decimal Form:

$0.70959234 \dots$