Simplify square root of 7x^2* square root of 12x^5

$\sqrt{7 x^{2}} \cdot \sqrt{12 x^{5}}$

Reorder $7$ and $x^{2}$ .

$\sqrt{x^{2} \cdot 7} \cdot \sqrt{12 x^{5}}$

Pull terms out from under the radical.

$x \sqrt{7} \cdot \sqrt{12 x^{5}}$

Rewrite $12 x^{5}$ as ${(2 x^{2})}^{2} \cdot (3 x)$ .

Factor $4$ out of $12$ .

$x \sqrt{7} \cdot \sqrt{4 (3) x^{5}}$

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

$x \sqrt{7} \cdot \sqrt{2^{2} \cdot 3 x^{5}}$

Factor out $x^{4}$ .

$x \sqrt{7} \cdot \sqrt{2^{2} \cdot 3 (x^{4} x)}$

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

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

Move $3$ .

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

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

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

Add parentheses.

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

Pull terms out from under the radical.

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

Multiply $x$ by $x^{2}$ by adding the exponents.

Move $x^{2}$ .

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

Multiply $x^{2}$ by $x$ .

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

$x^{2} x^{1} \sqrt{7} \cdot (2 \sqrt{3 x})$

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

$x^{2 + 1} \sqrt{7} \cdot (2 \sqrt{3 x})$

Add $2$ and $1$ .

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

Multiply $x^{3} \sqrt{7} (2 \sqrt{3 x})$ .

Combine using the product rule for radicals.

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

Multiply $7$ by $3$ .

$x^{3} (2 \sqrt{21 x})$

Rewrite using the commutative property of multiplication.

$2 x^{3} \sqrt{21 x}$