Basic Math Examples

$3 \sqrt{5} \cdot \sqrt{10} + 11 \sqrt{5} \cdot \sqrt{10} - \sqrt{5}$

Step 1

Simplify each term.

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Step 1.1

Multiply $3 \sqrt{5} \sqrt{10}$ .

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Step 1.1.1

Combine using the product rule for radicals.

$3 \sqrt{10 \cdot 5} + 11 \sqrt{5} \cdot \sqrt{10} - \sqrt{5}$

Step 1.1.2

Multiply $10$ by $5$ .

$3 \sqrt{50} + 11 \sqrt{5} \cdot \sqrt{10} - \sqrt{5}$

Step 1.2

Rewrite $50$ as $5^{2} \cdot 2$ .

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Step 1.2.1

Factor $25$ out of $50$ .

$3 \sqrt{25 (2)} + 11 \sqrt{5} \cdot \sqrt{10} - \sqrt{5}$

Step 1.2.2

Rewrite $25$ as $5^{2}$ .

$3 \sqrt{5^{2} \cdot 2} + 11 \sqrt{5} \cdot \sqrt{10} - \sqrt{5}$

Step 1.3

Pull terms out from under the radical.

$3 (5 \sqrt{2}) + 11 \sqrt{5} \cdot \sqrt{10} - \sqrt{5}$

Step 1.4

Multiply $5$ by $3$ .

$15 \sqrt{2} + 11 \sqrt{5} \cdot \sqrt{10} - \sqrt{5}$

Step 1.5

Multiply $11 \sqrt{5} \sqrt{10}$ .

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Step 1.5.1

Combine using the product rule for radicals.

$15 \sqrt{2} + 11 \sqrt{10 \cdot 5} - \sqrt{5}$

Step 1.5.2

Multiply $10$ by $5$ .

$15 \sqrt{2} + 11 \sqrt{50} - \sqrt{5}$

Step 1.6

Rewrite $50$ as $5^{2} \cdot 2$ .

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Step 1.6.1

Factor $25$ out of $50$ .

$15 \sqrt{2} + 11 \sqrt{25 (2)} - \sqrt{5}$

Step 1.6.2

Rewrite $25$ as $5^{2}$ .

$15 \sqrt{2} + 11 \sqrt{5^{2} \cdot 2} - \sqrt{5}$

Step 1.7

Pull terms out from under the radical.

$15 \sqrt{2} + 11 (5 \sqrt{2}) - \sqrt{5}$

Step 1.8

Multiply $5$ by $11$ .

$15 \sqrt{2} + 55 \sqrt{2} - \sqrt{5}$

Step 2

Add $15 \sqrt{2}$ and $55 \sqrt{2}$ .

$70 \sqrt{2} - \sqrt{5}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$70 \sqrt{2} - \sqrt{5}$

Decimal Form:

$96.75888138 \dots$