Algebra Examples

$\sqrt{5} \cdot 2 \sqrt{32} - 21 \sqrt{10}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $32$ as $4^{2} \cdot 2$ .

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Step 1.1.1

Factor $16$ out of $32$ .

$\sqrt{5} \cdot (2 \sqrt{16 (2)}) - 21 \sqrt{10}$

Step 1.1.2

Rewrite $16$ as $4^{2}$ .

$\sqrt{5} \cdot (2 \sqrt{4^{2} \cdot 2}) - 21 \sqrt{10}$

$\sqrt{5} \cdot (2 \sqrt{4^{2} \cdot 2}) - 21 \sqrt{10}$

Step 1.2

Pull terms out from under the radical.

$\sqrt{5} \cdot (2 (4 \sqrt{2})) - 21 \sqrt{10}$

Step 1.3

Multiply $4$ by $2$ .

$\sqrt{5} \cdot (8 \sqrt{2}) - 21 \sqrt{10}$

Step 1.4

Multiply $\sqrt{5} (8 \sqrt{2})$ .

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Step 1.4.1

Combine using the product rule for radicals.

$8 \sqrt{5 \cdot 2} - 21 \sqrt{10}$

Step 1.4.2

Multiply $5$ by $2$ .

$8 \sqrt{10} - 21 \sqrt{10}$

$8 \sqrt{10} - 21 \sqrt{10}$

$8 \sqrt{10} - 21 \sqrt{10}$

Step 2

Subtract $21 \sqrt{10}$ from $8 \sqrt{10}$ .

$- 13 \sqrt{10}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$- 13 \sqrt{10}$

Decimal Form:

$- 41.10960958 \dots$

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