Basic Math Examples

${(\sqrt{5} + m)}^{2}$

Step 1

Rewrite ${(\sqrt{5} + m)}^{2}$ as $(\sqrt{5} + m) (\sqrt{5} + m)$ .

$(\sqrt{5} + m) (\sqrt{5} + m)$

Step 2

Expand $(\sqrt{5} + m) (\sqrt{5} + m)$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

$\sqrt{5} (\sqrt{5} + m) + m (\sqrt{5} + m)$

Step 2.2

Apply the distributive property.

$\sqrt{5} \sqrt{5} + \sqrt{5} m + m (\sqrt{5} + m)$

Step 2.3

Apply the distributive property.

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

Step 3

Simplify and combine like terms.

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Step 3.1

Simplify each term.

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Step 3.1.1

Combine using the product rule for radicals.

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

Step 3.1.2

Multiply $5$ by $5$ .

$\sqrt{25} + \sqrt{5} m + m \sqrt{5} + m \cdot m$

Step 3.1.3

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

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

Step 3.1.4

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

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

Step 3.1.5

Multiply $m$ by $m$ .

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

Step 3.2

Reorder the factors of $\sqrt{5} m$ .

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

Step 3.3

Add $m \sqrt{5}$ and $m \sqrt{5}$ .

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