Evaluate cube root of 36x^2 square root of 12x square root of 9x^2

$\sqrt[3]{36 x^{2} \sqrt{12 x \sqrt{9 x^{2}}}}$

Step 1

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

$\sqrt[3]{36 x^{2} \sqrt{12 x \sqrt{{(3 x)}^{2}}}}$

Step 2

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

$\sqrt[3]{36 x^{2} \sqrt{12 x \cdot 3 x}}$

Step 3

Combine exponents.

Multiply $3$ by $12$ .

$\sqrt[3]{36 x^{2} \sqrt{36 x \cdot x}}$

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

$\sqrt[3]{36 x^{2} \sqrt{36 (x^{1} x)}}$

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

$\sqrt[3]{36 x^{2} \sqrt{36 (x^{1} x^{1})}}$

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

$\sqrt[3]{36 x^{2} \sqrt{36 x^{1 + 1}}}$

Add $1$ and $1$ .

$\sqrt[3]{36 x^{2} \sqrt{36 x^{2}}}$

Step 4

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

$\sqrt[3]{36 x^{2} \sqrt{{(6 x)}^{2}}}$

Step 5

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

$\sqrt[3]{36 x^{2} \cdot 6 x}$

Step 6

Combine exponents.

Multiply $6$ by $36$ .

$\sqrt[3]{216 x^{2} x}$

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

$\sqrt[3]{216 (x^{1} x^{2})}$

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

$\sqrt[3]{216 x^{1 + 2}}$

Add $1$ and $2$ .

$\sqrt[3]{216 x^{3}}$

Step 7

Rewrite $216 x^{3}$ as ${(6 x)}^{3}$ .

$\sqrt[3]{{(6 x)}^{3}}$

Step 8

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

$6 x$