Simplify square root of 5x^5* square root of 10a^2

$\sqrt{5 x^{5}} \cdot \sqrt{10 a^{2}}$

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

Factor out $x^{4}$ .

$\sqrt{5 (x^{4} x)} \cdot \sqrt{10 a^{2}}$

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

$\sqrt{5 ({(x^{2})}^{2} x)} \cdot \sqrt{10 a^{2}}$

Reorder $5$ and ${(x^{2})}^{2}$ .

$\sqrt{{(x^{2})}^{2} \cdot 5 x} \cdot \sqrt{10 a^{2}}$

Add parentheses.

$\sqrt{{(x^{2})}^{2} \cdot (5 x)} \cdot \sqrt{10 a^{2}}$

Pull terms out from under the radical.

$x^{2} \sqrt{5 x} \cdot \sqrt{10 a^{2}}$

Reorder $10$ and $a^{2}$ .

$x^{2} \sqrt{5 x} \cdot \sqrt{a^{2} \cdot 10}$

Pull terms out from under the radical.

$x^{2} \sqrt{5 x} \cdot (a \sqrt{10})$

Rewrite using the commutative property of multiplication.

$\sqrt{10} x^{2} \sqrt{5 x} a$

Multiply $\sqrt{10} x^{2} \sqrt{5 x}$ .

Combine using the product rule for radicals.

$x^{2} \sqrt{10 (5 x)} a$

Multiply $10$ by $5$ .

$x^{2} \sqrt{50 x} a$

Rewrite $50 x$ as $5^{2} \cdot (2 x)$ .

Factor $25$ out of $50$ .

$x^{2} \sqrt{25 (2) x} a$

Rewrite $25$ as $5^{2}$ .

$x^{2} \sqrt{5^{2} \cdot 2 x} a$

Add parentheses.

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

Pull terms out from under the radical.

$x^{2} (5 \sqrt{2 x}) a$

Rewrite using the commutative property of multiplication.

$5 x^{2} \sqrt{2 x} a$