Algebra Examples

$\sqrt{9} (\sqrt{3} + \sqrt{8})$

Step 1

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

$\sqrt{3^{2}} (\sqrt{3} + \sqrt{8})$

Step 2

Pull terms out from under the radical, assuming positive real numbers.

$3 (\sqrt{3} + \sqrt{8})$

Step 3

Simplify each term.

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Step 3.1

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

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Step 3.1.1

Factor $4$ out of $8$ .

$3 (\sqrt{3} + \sqrt{4 (2)})$

Step 3.1.2

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

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

Step 3.2

Pull terms out from under the radical.

$3 (\sqrt{3} + 2 \sqrt{2})$

Step 4

Simplify by multiplying through.

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Step 4.1

Apply the distributive property.

$3 \sqrt{3} + 3 (2 \sqrt{2})$

Step 4.2

Multiply $2$ by $3$ .

$3 \sqrt{3} + 6 \sqrt{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$3 \sqrt{3} + 6 \sqrt{2}$

Decimal Form:

$13.68143379 \dots$