Simplify 5 square root of 3a^2*3 square root of 25a

$5 \sqrt{3 a^{2}} \cdot 3 \sqrt{25 a}$

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

$5 \sqrt{a^{2} \cdot 3} \cdot (3 \sqrt{25 a})$

Pull terms out from under the radical.

$5 (a \sqrt{3}) \cdot (3 \sqrt{25 a})$

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

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

Pull terms out from under the radical.

$5 a \sqrt{3} \cdot (3 (5 \sqrt{a}))$

Multiply $5$ by $3$ .

$5 a \sqrt{3} \cdot (15 \sqrt{a})$

Multiply $5 a \sqrt{3} (15 \sqrt{a})$ .

Multiply $15$ by $5$ .

$75 a \sqrt{3} \sqrt{a}$

Combine using the product rule for radicals.

$75 a \sqrt{a \cdot 3}$

$75 a \sqrt{a \cdot 3}$

Reorder factors in $75 a \sqrt{a \cdot 3}$ .

$75 a \sqrt{3 a}$

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