Simplify the Radical Expression 8 square root of 3x* square root of 15x

$8 \sqrt{3 x} \cdot \sqrt{15 x}$

Step 1

Multiply $8 \sqrt{3 x} \sqrt{15 x}$ .

Combine using the product rule for radicals.

$8 \sqrt{15 x (3 x)}$

Multiply $3$ by $15$ .

$8 \sqrt{45 x \cdot x}$

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

$8 \sqrt{45 (x^{1} x)}$

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

$8 \sqrt{45 (x^{1} x^{1})}$

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

$8 \sqrt{45 x^{1 + 1}}$

Add $1$ and $1$ .

$8 \sqrt{45 x^{2}}$

Step 2

Rewrite $45 x^{2}$ as ${(3 x)}^{2} \cdot 5$ .

Factor $9$ out of $45$ .

$8 \sqrt{9 (5) x^{2}}$

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

$8 \sqrt{3^{2} \cdot 5 x^{2}}$

Move $5$ .

$8 \sqrt{3^{2} x^{2} \cdot 5}$

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

$8 \sqrt{{(3 x)}^{2} \cdot 5}$

Step 3

Pull terms out from under the radical.

$8 (| 3 x | \sqrt{5})$

Step 4

Remove non-negative terms from the absolute value.

$8 (3 | x | \sqrt{5})$

Step 5

Multiply $3$ by $8$ .

$24 | x | \sqrt{5}$