Simplify square root of 3x* square root of 51x^3

$\sqrt{3 x} \cdot \sqrt{51 x^{3}}$

Step 1

Rewrite $51 x^{3}$ as $x^{2} \cdot (51 x)$ .

Factor out $x^{2}$ .

$\sqrt{3 x} \cdot \sqrt{51 (x^{2} x)}$

Reorder $51$ and $x^{2}$ .

$\sqrt{3 x} \cdot \sqrt{x^{2} \cdot 51 x}$

Add parentheses.

$\sqrt{3 x} \cdot \sqrt{x^{2} \cdot (51 x)}$

Step 2

Pull terms out from under the radical.

$\sqrt{3 x} \cdot (x \sqrt{51 x})$

Step 3

Multiply $\sqrt{3 x} (x \sqrt{51 x})$ .

Combine using the product rule for radicals.

$x \sqrt{3 x (51 x)}$

Multiply $51$ by $3$ .

$x \sqrt{153 x \cdot x}$

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

$x \sqrt{153 (x^{1} x)}$

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

$x \sqrt{153 (x^{1} x^{1})}$

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

$x \sqrt{153 x^{1 + 1}}$

Add $1$ and $1$ .

$x \sqrt{153 x^{2}}$

Step 4

Rewrite $153 x^{2}$ as ${(3 x)}^{2} \cdot 17$ .

Factor $9$ out of $153$ .

$x \sqrt{9 (17) x^{2}}$

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

$x \sqrt{3^{2} \cdot 17 x^{2}}$

Move $17$ .

$x \sqrt{3^{2} x^{2} \cdot 17}$

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

$x \sqrt{{(3 x)}^{2} \cdot 17}$

Step 5

Pull terms out from under the radical.

$x (3 x \sqrt{17})$

Step 6

Rewrite using the commutative property of multiplication.

$3 \sqrt{17} x \cdot x$

Step 7

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$3 \sqrt{17} (x \cdot x)$

Multiply $x$ by $x$ .

$3 \sqrt{17} x^{2}$

Simplify square root of 3x* square root of 51x^3

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