Algebra Examples

$(\sqrt{2} + 2 \sqrt{8}) (3 \sqrt{6} - \sqrt{5})$

Step 1

Simplify each term.

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Step 1.1

Rewrite $8$ as $2^{2} \cdot 2$ .

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Step 1.1.1

Factor $4$ out of $8$ .

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

Step 1.1.2

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

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

Step 1.2

Pull terms out from under the radical.

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

Step 1.3

Multiply $2$ by $2$ .

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

Step 2

Simplify terms.

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Step 2.1

Add $\sqrt{2}$ and $4 \sqrt{2}$ .

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

Step 2.2

Apply the distributive property.

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

Step 3

Multiply $5 \sqrt{2} (3 \sqrt{6})$ .

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Step 3.1

Multiply $3$ by $5$ .

$15 \sqrt{2} \sqrt{6} + 5 \sqrt{2} (- \sqrt{5})$

Step 3.2

Combine using the product rule for radicals.

$15 \sqrt{6 \cdot 2} + 5 \sqrt{2} (- \sqrt{5})$

Step 3.3

Multiply $6$ by $2$ .

$15 \sqrt{12} + 5 \sqrt{2} (- \sqrt{5})$

Step 4

Multiply $5 \sqrt{2} (- \sqrt{5})$ .

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Step 4.1

Multiply $- 1$ by $5$ .

$15 \sqrt{12} - 5 \sqrt{2} \sqrt{5}$

Step 4.2

Combine using the product rule for radicals.

$15 \sqrt{12} - 5 \sqrt{5 \cdot 2}$

Step 4.3

Multiply $5$ by $2$ .

$15 \sqrt{12} - 5 \sqrt{10}$

Step 5

Simplify each term.

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Step 5.1

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

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Step 5.1.1

Factor $4$ out of $12$ .

$15 \sqrt{4 (3)} - 5 \sqrt{10}$

Step 5.1.2

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

$15 \sqrt{2^{2} \cdot 3} - 5 \sqrt{10}$

Step 5.2

Pull terms out from under the radical.

$15 (2 \sqrt{3}) - 5 \sqrt{10}$

Step 5.3

Multiply $2$ by $15$ .

$30 \sqrt{3} - 5 \sqrt{10}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$30 \sqrt{3} - 5 \sqrt{10}$

Decimal Form:

$36.15013592 \dots$