Finite Math Examples

$(6 \sqrt{5 - 8} \sqrt{6}) (\sqrt{5} - 6 \sqrt{6})$

Step 1

Subtract $8$ from $5$ .

$6 \sqrt{- 3} \sqrt{6} (\sqrt{5} - 6 \sqrt{6})$

Step 2

Rewrite $- 3$ as $- 1 (3)$ .

$6 \sqrt{- 1 (3)} \sqrt{6} (\sqrt{5} - 6 \sqrt{6})$

Step 3

Rewrite $\sqrt{- 1 (3)}$ as $\sqrt{- 1} \cdot \sqrt{3}$ .

$6 (\sqrt{- 1} \cdot \sqrt{3}) \sqrt{6} (\sqrt{5} - 6 \sqrt{6})$

Step 4

Rewrite $\sqrt{- 1}$ as $i$ .

$6 (i \cdot \sqrt{3}) \sqrt{6} (\sqrt{5} - 6 \sqrt{6})$

Step 5

Multiply $6 i \sqrt{3} \sqrt{6}$ .

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Step 5.1

Combine using the product rule for radicals.

$6 i \sqrt{6 \cdot 3} (\sqrt{5} - 6 \sqrt{6})$

Step 5.2

Multiply $6$ by $3$ .

$6 i \sqrt{18} (\sqrt{5} - 6 \sqrt{6})$

Step 6

Rewrite $18$ as $3^{2} \cdot 2$ .

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Step 6.1

Factor $9$ out of $18$ .

$6 i \sqrt{9 (2)} (\sqrt{5} - 6 \sqrt{6})$

Step 6.2

Rewrite $9$ as $3^{2}$ .

$6 i \sqrt{3^{2} \cdot 2} (\sqrt{5} - 6 \sqrt{6})$

Step 7

Pull terms out from under the radical.

$6 i (3 \sqrt{2}) (\sqrt{5} - 6 \sqrt{6})$

Step 8

Multiply $3$ by $6$ .

$18 i \sqrt{2} (\sqrt{5} - 6 \sqrt{6})$

Step 9

Apply the distributive property.

$18 i \sqrt{2} \sqrt{5} + 18 i \sqrt{2} (- 6 \sqrt{6})$

Step 10

Multiply $18 i \sqrt{2} \sqrt{5}$ .

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Step 10.1

Combine using the product rule for radicals.

$18 i \sqrt{5 \cdot 2} + 18 i \sqrt{2} (- 6 \sqrt{6})$

Step 10.2

Multiply $5$ by $2$ .

$18 i \sqrt{10} + 18 i \sqrt{2} (- 6 \sqrt{6})$

Step 11

Multiply $18 i \sqrt{2} (- 6 \sqrt{6})$ .

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Step 11.1

Multiply $- 6$ by $18$ .

$18 i \sqrt{10} - 108 i \sqrt{2} \sqrt{6}$

Step 11.2

Combine using the product rule for radicals.

$18 i \sqrt{10} - 108 i \sqrt{6 \cdot 2}$

Step 11.3

Multiply $6$ by $2$ .

$18 i \sqrt{10} - 108 i \sqrt{12}$

Step 12

Simplify each term.

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Step 12.1

Rewrite $12$ as $2^{2} \cdot 3$ .

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Step 12.1.1

Factor $4$ out of $12$ .

$18 i \sqrt{10} - 108 i \sqrt{4 (3)}$

Step 12.1.2

Rewrite $4$ as $2^{2}$ .

$18 i \sqrt{10} - 108 i \sqrt{2^{2} \cdot 3}$

Step 12.2

Pull terms out from under the radical.

$18 i \sqrt{10} - 108 i (2 \sqrt{3})$

Step 12.3

Multiply $2$ by $- 108$ .

$18 i \sqrt{10} - 216 i \sqrt{3}$