Simplify square root of 3x^4* square root of 24x^3

$\sqrt{3 x^{4}} \cdot \sqrt{24 x^{3}}$

Rewrite $3 x^{4}$ as ${(x^{2})}^{2} \cdot 3$ .

Tap for more steps…

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

$\sqrt{3 {(x^{2})}^{2}} \cdot \sqrt{24 x^{3}}$

Reorder $3$ and ${(x^{2})}^{2}$ .

$\sqrt{{(x^{2})}^{2} \cdot 3} \cdot \sqrt{24 x^{3}}$

Pull terms out from under the radical.

$x^{2} \sqrt{3} \cdot \sqrt{24 x^{3}}$

Rewrite $24 x^{3}$ as ${(2 x)}^{2} \cdot (6 x)$ .

Tap for more steps…

Factor $4$ out of $24$ .

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

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

$x^{2} \sqrt{3} \cdot \sqrt{2^{2} \cdot 6 x^{3}}$

Factor out $x^{2}$ .

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

Move $6$ .

$x^{2} \sqrt{3} \cdot \sqrt{2^{2} x^{2} \cdot 6 x}$

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

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

Add parentheses.

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

Pull terms out from under the radical.

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

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

Tap for more steps…

Move $x$ .

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

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

Tap for more steps…

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

$x^{1} x^{2} \sqrt{3} \cdot (2 \sqrt{6 x})$

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

$x^{1 + 2} \sqrt{3} \cdot (2 \sqrt{6 x})$

Add $1$ and $2$ .

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

Multiply $x^{3} \sqrt{3} (2 \sqrt{6 x})$ .

Tap for more steps…

Combine using the product rule for radicals.

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

Multiply $3$ by $6$ .

$x^{3} (2 \sqrt{18 x})$

Rewrite using the commutative property of multiplication.

$2 x^{3} \sqrt{18 x}$

Rewrite $18 x$ as $3^{2} \cdot (2 x)$ .

Tap for more steps…

Factor $9$ out of $18$ .

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

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

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

Add parentheses.

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

Pull terms out from under the radical.

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

Multiply $3$ by $2$ .

$6 x^{3} \sqrt{2 x}$

Simplify square root of 3x^4* square root of 24x^3

Download our
App from the store

Create a High Performed UI/UX Design from a Silicon Valley.

Download our App from the store

Create a High Performed UI/UX Design from a Silicon Valley.

Download our
App from the store