Pre-Algebra Examples

$\sqrt{5} \cdot (2 + \sqrt{5})$

Step 1

Simplify terms.

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Step 1.1

Apply the distributive property.

$\sqrt{5} \cdot 2 + \sqrt{5} \sqrt{5}$

Step 1.2

Move $2$ to the left of $\sqrt{5}$ .

$2 \cdot \sqrt{5} + \sqrt{5} \sqrt{5}$

Step 1.3

Combine using the product rule for radicals.

$2 \cdot \sqrt{5} + \sqrt{5 \cdot 5}$

Step 2

Simplify each term.

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Step 2.1

Multiply $5$ by $5$ .

$2 \sqrt{5} + \sqrt{25}$

Step 2.2

Rewrite $25$ as $5^{2}$ .

$2 \sqrt{5} + \sqrt{5^{2}}$

Step 2.3

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

$2 \sqrt{5} + 5$

Step 3

The result can be shown in multiple forms.

Exact Form:

$2 \sqrt{5} + 5$

Decimal Form:

$9.47213595 \dots$