Simplify 5 square root of 4a^2*3 square root of 25a

$5 \sqrt{4 a^{2}} \cdot 3 \sqrt{25 a}$

Step 1

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

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

Step 2

Pull terms out from under the radical, assuming positive real numbers.

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

Step 3

Write the expression using exponents.

Multiply $2$ by $5$ .

$10 a \cdot (3 \sqrt{25 a})$

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

$10 a \cdot (3 \sqrt{5^{2} a})$

Step 4

Pull terms out from under the radical.

$10 a \cdot (3 (5 \sqrt{a}))$

Step 5

Multiply.

Multiply $5$ by $3$ .

$10 a \cdot (15 \sqrt{a})$

Multiply $15$ by $10$ .

$150 a \sqrt{a}$