Simplify square root of 7( square root of 2+ square root of 3- square root of 5)

$\sqrt{7} (\sqrt{2} + \sqrt{3} - \sqrt{5})$

Step 1

Apply the distributive property.

$\sqrt{7} \sqrt{2} + \sqrt{7} \sqrt{3} + \sqrt{7} (- \sqrt{5})$

Step 2

Simplify.

Combine using the product rule for radicals.

$\sqrt{7 \cdot 2} + \sqrt{7} \sqrt{3} + \sqrt{7} (- \sqrt{5})$

Combine using the product rule for radicals.

$\sqrt{7 \cdot 2} + \sqrt{7 \cdot 3} + \sqrt{7} (- \sqrt{5})$

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

Combine using the product rule for radicals.

$\sqrt{7 \cdot 2} + \sqrt{7 \cdot 3} - \sqrt{7 \cdot 5}$

Multiply $7$ by $5$ .

$\sqrt{7 \cdot 2} + \sqrt{7 \cdot 3} - \sqrt{35}$

Step 3

Simplify each term.

Multiply $7$ by $2$ .

$\sqrt{14} + \sqrt{7 \cdot 3} - \sqrt{35}$

Multiply $7$ by $3$ .

$\sqrt{14} + \sqrt{21} - \sqrt{35}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\sqrt{14} + \sqrt{21} - \sqrt{35}$

Decimal Form:

$2.40815329 \dots$