Algebra Examples

$3 \sqrt{10} (5 \sqrt{2} - 6 \sqrt{8})$

Step 1

Simplify each term.

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Step 1.1

Rewrite $8$ as $2^{2} \cdot 2$ .

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Step 1.1.1

Factor $4$ out of $8$ .

$3 \sqrt{10} (5 \sqrt{2} - 6 \sqrt{4 (2)})$

Step 1.1.2

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

$3 \sqrt{10} (5 \sqrt{2} - 6 \sqrt{2^{2} \cdot 2})$

Step 1.2

Pull terms out from under the radical.

$3 \sqrt{10} (5 \sqrt{2} - 6 (| 2 | \sqrt{2}))$

Step 1.3

The absolute value is the distance between a number and zero. The distance between $0$ and $2$ is $2$ .

$3 \sqrt{10} (5 \sqrt{2} - 6 (2 \sqrt{2}))$

Step 1.4

Multiply $2$ by $- 6$ .

$3 \sqrt{10} (5 \sqrt{2} - 12 \sqrt{2})$

Step 2

Subtract $12 \sqrt{2}$ from $5 \sqrt{2}$ .

$3 \sqrt{10} (- 7 \sqrt{2})$

Step 3

Multiply $3 \sqrt{10} (- 7 \sqrt{2})$ .

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Step 3.1

Multiply $- 7$ by $3$ .

$- 21 \sqrt{10} \sqrt{2}$

Step 3.2

Combine using the product rule for radicals.

$- 21 \sqrt{2 \cdot 10}$

Step 3.3

Multiply $2$ by $10$ .

$- 21 \sqrt{20}$

Step 4

Rewrite $20$ as $2^{2} \cdot 5$ .

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Step 4.1

Factor $4$ out of $20$ .

$- 21 \sqrt{4 (5)}$

Step 4.2

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

$- 21 \sqrt{2^{2} \cdot 5}$

Step 5

Pull terms out from under the radical.

$- 21 (| 2 | \sqrt{5})$

Step 6

The absolute value is the distance between a number and zero. The distance between $0$ and $2$ is $2$ .

$- 21 (2 \sqrt{5})$

Step 7

Multiply $2$ by $- 21$ .

$- 42 \sqrt{5}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$- 42 \sqrt{5}$

Decimal Form:

$- 93.91485505 \dots$