Algebra Examples

$\sqrt{9 x \sqrt{8 x \sqrt[3]{8 x^{3}}}}$

Step 1

Rewrite $8 x^{3}$ as ${(2 x)}^{3}$ .

$\sqrt{9 x \sqrt{8 x \sqrt[3]{{(2 x)}^{3}}}}$

Step 2

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

$\sqrt{9 x \sqrt{8 x \cdot 2 x}}$

Step 3

Combine exponents.

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Step 3.1

Multiply $2$ by $8$ .

$\sqrt{9 x \sqrt{16 x \cdot x}}$

Step 3.2

Raise $x$ to the power of $1$ .

$\sqrt{9 x \sqrt{16 (x^{1} x)}}$

Step 3.3

Raise $x$ to the power of $1$ .

$\sqrt{9 x \sqrt{16 (x^{1} x^{1})}}$

Step 3.4

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\sqrt{9 x \sqrt{16 x^{1 + 1}}}$

Step 3.5

Add $1$ and $1$ .

$\sqrt{9 x \sqrt{16 x^{2}}}$

Step 4

Rewrite $16 x^{2}$ as ${(4 x)}^{2}$ .

$\sqrt{9 x \sqrt{{(4 x)}^{2}}}$

Step 5

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

$\sqrt{9 x \cdot 4 x}$

Step 6

Combine exponents.

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Step 6.1

Multiply $4$ by $9$ .

$\sqrt{36 x \cdot x}$

Step 6.2

Raise $x$ to the power of $1$ .

$\sqrt{36 (x^{1} x)}$

Step 6.3

Raise $x$ to the power of $1$ .

$\sqrt{36 (x^{1} x^{1})}$

Step 6.4

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\sqrt{36 x^{1 + 1}}$

Step 6.5

Add $1$ and $1$ .

$\sqrt{36 x^{2}}$

Step 7

Rewrite $36 x^{2}$ as ${(6 x)}^{2}$ .

$\sqrt{{(6 x)}^{2}}$

Step 8

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

$6 x$