Linear Algebra Examples

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

Step 1

Subtract $2$ from $10$ .

$5 \sqrt{8} (4 \sqrt{6 + 3})$

Step 2

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

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Step 2.1

Factor $4$ out of $8$ .

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

Step 2.2

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

$5 \sqrt{2^{2} \cdot 2} (4 \sqrt{6 + 3})$

Step 3

Pull terms out from under the radical.

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

Step 4

Simplify the expression.

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Step 4.1

Multiply $2$ by $5$ .

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

Step 4.2

Add $6$ and $3$ .

$10 \sqrt{2} (4 \sqrt{9})$

Step 4.3

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

$10 \sqrt{2} (4 \sqrt{3^{2}})$

Step 5

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

$10 \sqrt{2} (4 \cdot 3)$

Step 6

Multiply $4$ by $3$ .

$10 \sqrt{2} \cdot 12$

Step 7

Multiply $12$ by $10$ .

$120 \sqrt{2}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$120 \sqrt{2}$

Decimal Form:

$169.70562748 \dots$