Basic Math Examples

$(\sqrt{13} + \sqrt{715}) (\sqrt{55} + \sqrt{11})$

Step 1

Expand $(\sqrt{13} + \sqrt{715}) (\sqrt{55} + \sqrt{11})$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$\sqrt{13} (\sqrt{55} + \sqrt{11}) + \sqrt{715} (\sqrt{55} + \sqrt{11})$

Step 1.2

Apply the distributive property.

$\sqrt{13} \sqrt{55} + \sqrt{13} \sqrt{11} + \sqrt{715} (\sqrt{55} + \sqrt{11})$

Step 1.3

Apply the distributive property.

$\sqrt{13} \sqrt{55} + \sqrt{13} \sqrt{11} + \sqrt{715} \sqrt{55} + \sqrt{715} \sqrt{11}$

Step 2

Simplify each term.

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Step 2.1

Combine using the product rule for radicals.

$\sqrt{13 \cdot 55} + \sqrt{13} \sqrt{11} + \sqrt{715} \sqrt{55} + \sqrt{715} \sqrt{11}$

Step 2.2

Multiply $13$ by $55$ .

$\sqrt{715} + \sqrt{13} \sqrt{11} + \sqrt{715} \sqrt{55} + \sqrt{715} \sqrt{11}$

Step 2.3

Combine using the product rule for radicals.

$\sqrt{715} + \sqrt{13 \cdot 11} + \sqrt{715} \sqrt{55} + \sqrt{715} \sqrt{11}$

Step 2.4

Multiply $13$ by $11$ .

$\sqrt{715} + \sqrt{143} + \sqrt{715} \sqrt{55} + \sqrt{715} \sqrt{11}$

Step 2.5

Combine using the product rule for radicals.

$\sqrt{715} + \sqrt{143} + \sqrt{715 \cdot 55} + \sqrt{715} \sqrt{11}$

Step 2.6

Multiply $715$ by $55$ .

$\sqrt{715} + \sqrt{143} + \sqrt{39325} + \sqrt{715} \sqrt{11}$

Step 2.7

Rewrite $39325$ as $55^{2} \cdot 13$ .

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Step 2.7.1

Factor $3025$ out of $39325$ .

$\sqrt{715} + \sqrt{143} + \sqrt{3025 (13)} + \sqrt{715} \sqrt{11}$

Step 2.7.2

Rewrite $3025$ as $55^{2}$ .

$\sqrt{715} + \sqrt{143} + \sqrt{55^{2} \cdot 13} + \sqrt{715} \sqrt{11}$

Step 2.8

Pull terms out from under the radical.

$\sqrt{715} + \sqrt{143} + 55 \sqrt{13} + \sqrt{715} \sqrt{11}$

Step 2.9

Combine using the product rule for radicals.

$\sqrt{715} + \sqrt{143} + 55 \sqrt{13} + \sqrt{715 \cdot 11}$

Step 2.10

Multiply $715$ by $11$ .

$\sqrt{715} + \sqrt{143} + 55 \sqrt{13} + \sqrt{7865}$

Step 2.11

Rewrite $7865$ as $11^{2} \cdot 65$ .

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Step 2.11.1

Factor $121$ out of $7865$ .

$\sqrt{715} + \sqrt{143} + 55 \sqrt{13} + \sqrt{121 (65)}$

Step 2.11.2

Rewrite $121$ as $11^{2}$ .

$\sqrt{715} + \sqrt{143} + 55 \sqrt{13} + \sqrt{11^{2} \cdot 65}$

Step 2.12

Pull terms out from under the radical.

$\sqrt{715} + \sqrt{143} + 55 \sqrt{13} + 11 \sqrt{65}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\sqrt{715} + \sqrt{143} + 55 \sqrt{13} + 11 \sqrt{65}$

Decimal Form:

$325.68790003 \dots$