Algebra Examples

$3 \sqrt{18} + 5 \sqrt{50}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $18$ as $3^{2} \cdot 2$ .

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Step 1.1.1

Factor $9$ out of $18$ .

$3 \sqrt{9 (2)} + 5 \sqrt{50}$

Step 1.1.2

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

$3 \sqrt{3^{2} \cdot 2} + 5 \sqrt{50}$

$3 \sqrt{3^{2} \cdot 2} + 5 \sqrt{50}$

Step 1.2

Pull terms out from under the radical.

$3 (3 \sqrt{2}) + 5 \sqrt{50}$

Step 1.3

Multiply $3$ by $3$ .

$9 \sqrt{2} + 5 \sqrt{50}$

Step 1.4

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

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Step 1.4.1

Factor $25$ out of $50$ .

$9 \sqrt{2} + 5 \sqrt{25 (2)}$

Step 1.4.2

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

$9 \sqrt{2} + 5 \sqrt{5^{2} \cdot 2}$

$9 \sqrt{2} + 5 \sqrt{5^{2} \cdot 2}$

Step 1.5

Pull terms out from under the radical.

$9 \sqrt{2} + 5 (5 \sqrt{2})$

Step 1.6

Multiply $5$ by $5$ .

$9 \sqrt{2} + 25 \sqrt{2}$

$9 \sqrt{2} + 25 \sqrt{2}$

Step 2

Add $9 \sqrt{2}$ and $25 \sqrt{2}$ .

$34 \sqrt{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$34 \sqrt{2}$

Decimal Form:

$48.08326112 \dots$

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