Basic Math Examples

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

Step 1

Expand $(\sqrt{5} + 5) (2 \sqrt{10} + 3)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

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

Step 1.2

Apply the distributive property.

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

Step 1.3

Apply the distributive property.

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

Step 2

Simplify each term.

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Step 2.1

Multiply $\sqrt{5} (2 \sqrt{10})$ .

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Step 2.1.1

Combine using the product rule for radicals.

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

Step 2.1.2

Multiply $5$ by $10$ .

$2 \sqrt{50} + \sqrt{5} \cdot 3 + 5 (2 \sqrt{10}) + 5 \cdot 3$

Step 2.2

Rewrite $50$ as $5^{2} \cdot 2$ .

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Step 2.2.1

Factor $25$ out of $50$ .

$2 \sqrt{25 (2)} + \sqrt{5} \cdot 3 + 5 (2 \sqrt{10}) + 5 \cdot 3$

Step 2.2.2

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

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

Step 2.3

Pull terms out from under the radical.

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

Step 2.4

Multiply $5$ by $2$ .

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

Step 2.5

Move $3$ to the left of $\sqrt{5}$ .

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

Step 2.6

Multiply $2$ by $5$ .

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

Step 2.7

Multiply $5$ by $3$ .

$10 \sqrt{2} + 3 \sqrt{5} + 10 \sqrt{10} + 15$

Step 3

The result can be shown in multiple forms.

Exact Form:

$10 \sqrt{2} + 3 \sqrt{5} + 10 \sqrt{10} + 15$

Decimal Form:

$67.47311615 \dots$