Basic Math Examples

$5 \sqrt{10} \cdot \sqrt{5} + 1 \sqrt{2}$

Step 1

Simplify each term.

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Step 1.1

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

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Step 1.1.1

Combine using the product rule for radicals.

$5 \sqrt{5 \cdot 10} + 1 \sqrt{2}$

Step 1.1.2

Multiply $5$ by $10$ .

$5 \sqrt{50} + 1 \sqrt{2}$

$5 \sqrt{50} + 1 \sqrt{2}$

Step 1.2

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

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Step 1.2.1

Factor $25$ out of $50$ .

$5 \sqrt{25 (2)} + 1 \sqrt{2}$

Step 1.2.2

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

$5 \sqrt{5^{2} \cdot 2} + 1 \sqrt{2}$

$5 \sqrt{5^{2} \cdot 2} + 1 \sqrt{2}$

Step 1.3

Pull terms out from under the radical.

$5 (5 \sqrt{2}) + 1 \sqrt{2}$

Step 1.4

Multiply $5$ by $5$ .

$25 \sqrt{2} + 1 \sqrt{2}$

Step 1.5

Multiply $\sqrt{2}$ by $1$ .

$25 \sqrt{2} + \sqrt{2}$

$25 \sqrt{2} + \sqrt{2}$

Step 2

Add $25 \sqrt{2}$ and $\sqrt{2}$ .

$26 \sqrt{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$26 \sqrt{2}$

Decimal Form:

$36.76955262 \dots$

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