Algebra Examples

Simplify $(\sqrt{21} + 3) (\sqrt{21} + 8)$

Step 1

Expand $(\sqrt{21} + 3) (\sqrt{21} + 8)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$\sqrt{21} (\sqrt{21} + 8) + 3 (\sqrt{21} + 8)$

Step 1.2

Apply the distributive property.

$\sqrt{21} \sqrt{21} + \sqrt{21} \cdot 8 + 3 (\sqrt{21} + 8)$

Step 1.3

Apply the distributive property.

$\sqrt{21} \sqrt{21} + \sqrt{21} \cdot 8 + 3 \sqrt{21} + 3 \cdot 8$

Step 2

Simplify and combine like terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

Combine using the product rule for radicals.

$\sqrt{21 \cdot 21} + \sqrt{21} \cdot 8 + 3 \sqrt{21} + 3 \cdot 8$

Step 2.1.2

Multiply $21$ by $21$ .

$\sqrt{441} + \sqrt{21} \cdot 8 + 3 \sqrt{21} + 3 \cdot 8$

Step 2.1.3

Rewrite $441$ as $21^{2}$ .

$\sqrt{21^{2}} + \sqrt{21} \cdot 8 + 3 \sqrt{21} + 3 \cdot 8$

Step 2.1.4

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

$21 + \sqrt{21} \cdot 8 + 3 \sqrt{21} + 3 \cdot 8$

Step 2.1.5

Move $8$ to the left of $\sqrt{21}$ .

$21 + 8 \cdot \sqrt{21} + 3 \sqrt{21} + 3 \cdot 8$

Step 2.1.6

Multiply $3$ by $8$ .

$21 + 8 \sqrt{21} + 3 \sqrt{21} + 24$

Step 2.2

Add $21$ and $24$ .

$45 + 8 \sqrt{21} + 3 \sqrt{21}$

Step 2.3

Add $8 \sqrt{21}$ and $3 \sqrt{21}$ .

$45 + 11 \sqrt{21}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$45 + 11 \sqrt{21}$

Decimal Form:

$95.40833264 \dots$