Algebra Examples

$5 \sqrt{24 x^{5}} + 4 \sqrt{54 x^{5}}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $24 x^{5}$ as ${(2 x^{2})}^{2} \cdot (6 x)$ .

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Step 1.1.1

Factor $4$ out of $24$ .

$5 \sqrt{4 (6) x^{5}} + 4 \sqrt{54 x^{5}}$

Step 1.1.2

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

$5 \sqrt{2^{2} \cdot 6 x^{5}} + 4 \sqrt{54 x^{5}}$

Step 1.1.3

Factor out $x^{4}$ .

$5 \sqrt{2^{2} \cdot 6 (x^{4} x)} + 4 \sqrt{54 x^{5}}$

Step 1.1.4

Rewrite $x^{4}$ as ${(x^{2})}^{2}$ .

$5 \sqrt{2^{2} \cdot 6 ({(x^{2})}^{2} x)} + 4 \sqrt{54 x^{5}}$

Step 1.1.5

Move $6$ .

$5 \sqrt{2^{2} {(x^{2})}^{2} \cdot 6 x} + 4 \sqrt{54 x^{5}}$

Step 1.1.6

Rewrite $2^{2} {(x^{2})}^{2}$ as ${(2 x^{2})}^{2}$ .

$5 \sqrt{{(2 x^{2})}^{2} \cdot 6 x} + 4 \sqrt{54 x^{5}}$

Step 1.1.7

Add parentheses.

$5 \sqrt{{(2 x^{2})}^{2} \cdot (6 x)} + 4 \sqrt{54 x^{5}}$

Step 1.2

Pull terms out from under the radical.

$5 (2 x^{2} \sqrt{6 x}) + 4 \sqrt{54 x^{5}}$

Step 1.3

Multiply $2$ by $5$ .

$10 (x^{2} \sqrt{6 x}) + 4 \sqrt{54 x^{5}}$

Step 1.4

Rewrite $54 x^{5}$ as ${(3 x^{2})}^{2} \cdot (6 x)$ .

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Step 1.4.1

Factor $9$ out of $54$ .

$10 x^{2} \sqrt{6 x} + 4 \sqrt{9 (6) x^{5}}$

Step 1.4.2

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

$10 x^{2} \sqrt{6 x} + 4 \sqrt{3^{2} \cdot 6 x^{5}}$

Step 1.4.3

Factor out $x^{4}$ .

$10 x^{2} \sqrt{6 x} + 4 \sqrt{3^{2} \cdot 6 (x^{4} x)}$

Step 1.4.4

Rewrite $x^{4}$ as ${(x^{2})}^{2}$ .

$10 x^{2} \sqrt{6 x} + 4 \sqrt{3^{2} \cdot 6 ({(x^{2})}^{2} x)}$

Step 1.4.5

Move $6$ .

$10 x^{2} \sqrt{6 x} + 4 \sqrt{3^{2} {(x^{2})}^{2} \cdot 6 x}$

Step 1.4.6

Rewrite $3^{2} {(x^{2})}^{2}$ as ${(3 x^{2})}^{2}$ .

$10 x^{2} \sqrt{6 x} + 4 \sqrt{{(3 x^{2})}^{2} \cdot 6 x}$

Step 1.4.7

Add parentheses.

$10 x^{2} \sqrt{6 x} + 4 \sqrt{{(3 x^{2})}^{2} \cdot (6 x)}$

Step 1.5

Pull terms out from under the radical.

$10 x^{2} \sqrt{6 x} + 4 (3 x^{2} \sqrt{6 x})$

Step 1.6

Multiply $3$ by $4$ .

$10 x^{2} \sqrt{6 x} + 12 x^{2} \sqrt{6 x}$

Step 2

Add $10 x^{2} \sqrt{6 x}$ and $12 x^{2} \sqrt{6 x}$ .

$22 x^{2} \sqrt{6 x}$