Simplify ( square root of 10+ square root of 6)( square root of 30- square root of 18)

$(\sqrt{10} + \sqrt{6}) (\sqrt{30} - \sqrt{18})$

Simplify each term.

Rewrite $18$ as $3^{2} \cdot 2$ .

Factor $9$ out of $18$ .

$(\sqrt{10} + \sqrt{6}) (\sqrt{30} - \sqrt{9 (2)})$

Rewrite $9$ as $3^{2}$ .

$(\sqrt{10} + \sqrt{6}) (\sqrt{30} - \sqrt{3^{2} \cdot 2})$

Pull terms out from under the radical.

$(\sqrt{10} + \sqrt{6}) (\sqrt{30} - (3 \sqrt{2}))$

Multiply $3$ by $- 1$ .

$(\sqrt{10} + \sqrt{6}) (\sqrt{30} - 3 \sqrt{2})$

Expand $(\sqrt{10} + \sqrt{6}) (\sqrt{30} - 3 \sqrt{2})$ using the FOIL Method.

Apply the distributive property.

$\sqrt{10} (\sqrt{30} - 3 \sqrt{2}) + \sqrt{6} (\sqrt{30} - 3 \sqrt{2})$

Apply the distributive property.

$\sqrt{10} \sqrt{30} + \sqrt{10} (- 3 \sqrt{2}) + \sqrt{6} (\sqrt{30} - 3 \sqrt{2})$

Apply the distributive property.

$\sqrt{10} \sqrt{30} + \sqrt{10} (- 3 \sqrt{2}) + \sqrt{6} \sqrt{30} + \sqrt{6} (- 3 \sqrt{2})$

Simplify and combine like terms.

Simplify each term.

Combine using the product rule for radicals.

$\sqrt{10 \cdot 30} + \sqrt{10} (- 3 \sqrt{2}) + \sqrt{6} \sqrt{30} + \sqrt{6} (- 3 \sqrt{2})$

Multiply $10$ by $30$ .

$\sqrt{300} + \sqrt{10} (- 3 \sqrt{2}) + \sqrt{6} \sqrt{30} + \sqrt{6} (- 3 \sqrt{2})$

Rewrite $300$ as $10^{2} \cdot 3$ .

Factor $100$ out of $300$ .

$\sqrt{100 (3)} + \sqrt{10} (- 3 \sqrt{2}) + \sqrt{6} \sqrt{30} + \sqrt{6} (- 3 \sqrt{2})$

Rewrite $100$ as $10^{2}$ .

$\sqrt{10^{2} \cdot 3} + \sqrt{10} (- 3 \sqrt{2}) + \sqrt{6} \sqrt{30} + \sqrt{6} (- 3 \sqrt{2})$

Pull terms out from under the radical.

$10 \sqrt{3} + \sqrt{10} (- 3 \sqrt{2}) + \sqrt{6} \sqrt{30} + \sqrt{6} (- 3 \sqrt{2})$

Multiply $\sqrt{10} (- 3 \sqrt{2})$ .

Combine using the product rule for radicals.

$10 \sqrt{3} - 3 \sqrt{10 \cdot 2} + \sqrt{6} \sqrt{30} + \sqrt{6} (- 3 \sqrt{2})$

Multiply $10$ by $2$ .

$10 \sqrt{3} - 3 \sqrt{20} + \sqrt{6} \sqrt{30} + \sqrt{6} (- 3 \sqrt{2})$

Rewrite $20$ as $2^{2} \cdot 5$ .

Factor $4$ out of $20$ .

$10 \sqrt{3} - 3 \sqrt{4 (5)} + \sqrt{6} \sqrt{30} + \sqrt{6} (- 3 \sqrt{2})$

Rewrite $4$ as $2^{2}$ .

$10 \sqrt{3} - 3 \sqrt{2^{2} \cdot 5} + \sqrt{6} \sqrt{30} + \sqrt{6} (- 3 \sqrt{2})$

Pull terms out from under the radical.

$10 \sqrt{3} - 3 (2 \sqrt{5}) + \sqrt{6} \sqrt{30} + \sqrt{6} (- 3 \sqrt{2})$

Multiply $2$ by $- 3$ .

$10 \sqrt{3} - 6 \sqrt{5} + \sqrt{6} \sqrt{30} + \sqrt{6} (- 3 \sqrt{2})$

Combine using the product rule for radicals.

$10 \sqrt{3} - 6 \sqrt{5} + \sqrt{6 \cdot 30} + \sqrt{6} (- 3 \sqrt{2})$

Multiply $6$ by $30$ .

$10 \sqrt{3} - 6 \sqrt{5} + \sqrt{180} + \sqrt{6} (- 3 \sqrt{2})$

Rewrite $180$ as $6^{2} \cdot 5$ .

Factor $36$ out of $180$ .

$10 \sqrt{3} - 6 \sqrt{5} + \sqrt{36 (5)} + \sqrt{6} (- 3 \sqrt{2})$

Rewrite $36$ as $6^{2}$ .

$10 \sqrt{3} - 6 \sqrt{5} + \sqrt{6^{2} \cdot 5} + \sqrt{6} (- 3 \sqrt{2})$

Pull terms out from under the radical.

$10 \sqrt{3} - 6 \sqrt{5} + 6 \sqrt{5} + \sqrt{6} (- 3 \sqrt{2})$

Multiply $\sqrt{6} (- 3 \sqrt{2})$ .

Combine using the product rule for radicals.

$10 \sqrt{3} - 6 \sqrt{5} + 6 \sqrt{5} - 3 \sqrt{6 \cdot 2}$

Multiply $6$ by $2$ .

$10 \sqrt{3} - 6 \sqrt{5} + 6 \sqrt{5} - 3 \sqrt{12}$

Rewrite $12$ as $2^{2} \cdot 3$ .

Factor $4$ out of $12$ .

$10 \sqrt{3} - 6 \sqrt{5} + 6 \sqrt{5} - 3 \sqrt{4 (3)}$

Rewrite $4$ as $2^{2}$ .

$10 \sqrt{3} - 6 \sqrt{5} + 6 \sqrt{5} - 3 \sqrt{2^{2} \cdot 3}$

Pull terms out from under the radical.

$10 \sqrt{3} - 6 \sqrt{5} + 6 \sqrt{5} - 3 (2 \sqrt{3})$

Multiply $2$ by $- 3$ .

$10 \sqrt{3} - 6 \sqrt{5} + 6 \sqrt{5} - 6 \sqrt{3}$

Subtract $6 \sqrt{3}$ from $10 \sqrt{3}$ .

$4 \sqrt{3} - 6 \sqrt{5} + 6 \sqrt{5}$

Add $- 6 \sqrt{5}$ and $6 \sqrt{5}$ .

$4 \sqrt{3} + 0$

Add $4 \sqrt{3}$ and $0$ .

$4 \sqrt{3}$

The result can be shown in multiple forms.

Exact Form:

$4 \sqrt{3}$

Decimal Form:

$6.92820323 \dots$

Simplify ( square root of 10+ square root of 6)( square root of 30- square root of 18)

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