Pre-Algebra Examples

$\sqrt{24 x} + \sqrt{54 x}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $24 x$ as $2^{2} \cdot (6 x)$ .

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Step 1.1.1

Factor $4$ out of $24$ .

$\sqrt{4 (6) x} + \sqrt{54 x}$

Step 1.1.2

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

$\sqrt{2^{2} \cdot 6 x} + \sqrt{54 x}$

Step 1.1.3

Add parentheses.

$\sqrt{2^{2} \cdot (6 x)} + \sqrt{54 x}$

$\sqrt{2^{2} \cdot (6 x)} + \sqrt{54 x}$

Step 1.2

Pull terms out from under the radical.

$2 \sqrt{6 x} + \sqrt{54 x}$

Step 1.3

Rewrite $54 x$ as $3^{2} \cdot (6 x)$ .

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Step 1.3.1

Factor $9$ out of $54$ .

$2 \sqrt{6 x} + \sqrt{9 (6) x}$

Step 1.3.2

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

$2 \sqrt{6 x} + \sqrt{3^{2} \cdot 6 x}$

Step 1.3.3

Add parentheses.

$2 \sqrt{6 x} + \sqrt{3^{2} \cdot (6 x)}$

$2 \sqrt{6 x} + \sqrt{3^{2} \cdot (6 x)}$

Step 1.4

Pull terms out from under the radical.

$2 \sqrt{6 x} + 3 \sqrt{6 x}$

$2 \sqrt{6 x} + 3 \sqrt{6 x}$

Step 2

Add $2 \sqrt{6 x}$ and $3 \sqrt{6 x}$ .

$5 \sqrt{6 x}$

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