Algebra Examples

$\sqrt[4]{9 x^{2}} + 7 \sqrt{12 x}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $9 x^{2}$ as ${(3 x)}^{2}$ .

$\sqrt[4]{{(3 x)}^{2}} + 7 \sqrt{12 x}$

Step 1.2

Rewrite $\sqrt[4]{{(3 x)}^{2}}$ as $\sqrt{\sqrt{{(3 x)}^{2}}}$ .

$\sqrt{\sqrt{{(3 x)}^{2}}} + 7 \sqrt{12 x}$

Step 1.3

Pull terms out from under the radical, assuming positive real numbers.

$\sqrt{3 x} + 7 \sqrt{12 x}$

Step 1.4

Rewrite $12 x$ as $2^{2} \cdot (3 x)$ .

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Step 1.4.1

Factor $4$ out of $12$ .

$\sqrt{3 x} + 7 \sqrt{4 (3) x}$

Step 1.4.2

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

$\sqrt{3 x} + 7 \sqrt{2^{2} \cdot 3 x}$

Step 1.4.3

Add parentheses.

$\sqrt{3 x} + 7 \sqrt{2^{2} \cdot (3 x)}$

Step 1.5

Pull terms out from under the radical.

$\sqrt{3 x} + 7 (2 \sqrt{3 x})$

Step 1.6

Multiply $2$ by $7$ .

$\sqrt{3 x} + 14 \sqrt{3 x}$

Step 2

Add $\sqrt{3 x}$ and $14 \sqrt{3 x}$ .

$15 \sqrt{3 x}$