Simplify square root of 3x^2*3 square root of 3x^4

$\sqrt{3 x^{2}} \cdot 3 \sqrt{3 x^{4}}$

Step 1

Simplify the expression.

Rewrite using the commutative property of multiplication.

$3 \sqrt{3 x^{2}} \sqrt{3 x^{4}}$

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

$3 \sqrt{x^{2} \cdot 3} \sqrt{3 x^{4}}$

Step 2

Pull terms out from under the radical.

$3 (x \sqrt{3}) \sqrt{3 x^{4}}$

Step 3

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

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

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

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

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

Step 4

Pull terms out from under the radical.

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

Step 5

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

Move $x^{2}$ .

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

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

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

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

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

$3 x^{2 + 1} \sqrt{3} \sqrt{3}$

Add $2$ and $1$ .

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

Step 6

Multiply $3 x^{3} \sqrt{3} \sqrt{3}$ .

Raise $\sqrt{3}$ to the power of $1$ .

$3 x^{3} ({\sqrt{3}}^{1} \sqrt{3})$

Raise $\sqrt{3}$ to the power of $1$ .

$3 x^{3} ({\sqrt{3}}^{1} {\sqrt{3}}^{1})$

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

$3 x^{3} {\sqrt{3}}^{1 + 1}$

Add $1$ and $1$ .

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

Step 7

Rewrite ${\sqrt{3}}^{2}$ as $3$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3}$ as $3^{\frac{1}{2}}$ .

$3 x^{3} {(3^{\frac{1}{2}})}^{2}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$3 x^{3} \cdot 3^{\frac{1}{2} \cdot 2}$

Combine $\frac{1}{2}$ and $2$ .

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

$3 x^{3} \cdot 3^{1}$

Evaluate the exponent.

$3 x^{3} \cdot 3$

Step 8

Multiply $3$ by $3$ .

$9 x^{3}$

Simplify square root of 3x^2*3 square root of 3x^4

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