Algebra Examples

$5 \sqrt{20} \cdot 3 \sqrt{8}$

Step 1

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

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Step 1.1

Factor $4$ out of $20$ .

$5 \sqrt{4 (5)} \cdot (3 \sqrt{8})$

Step 1.2

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

$5 \sqrt{2^{2} \cdot 5} \cdot (3 \sqrt{8})$

$5 \sqrt{2^{2} \cdot 5} \cdot (3 \sqrt{8})$

Step 2

Pull terms out from under the radical.

$5 (2 \sqrt{5}) \cdot (3 \sqrt{8})$

Step 3

Multiply $2$ by $5$ .

$10 \sqrt{5} \cdot (3 \sqrt{8})$

Step 4

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

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Step 4.1

Factor $4$ out of $8$ .

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

Step 4.2

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

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

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

Step 5

Pull terms out from under the radical.

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

Step 6

Multiply $2$ by $3$ .

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

Step 7

Multiply $10 \sqrt{5} (6 \sqrt{2})$ .

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Step 7.1

Multiply $6$ by $10$ .

$60 \sqrt{5} \sqrt{2}$

Step 7.2

Combine using the product rule for radicals.

$60 \sqrt{2 \cdot 5}$

Step 7.3

Multiply $2$ by $5$ .

$60 \sqrt{10}$

$60 \sqrt{10}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$60 \sqrt{10}$

Decimal Form:

$189.73665961 \dots$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$