Question

$\sqrt{3x^{2}z^{3}}\cdot\sqrt{15x^{2}z}$

Explanation:

Step1: Combine the square roots

$\sqrt{3x^2z^3} \cdot \sqrt{15x^2z} = \sqrt{(3x^2z^3)(15x^2z)}$

Step2: Multiply the radicand terms

$\sqrt{3 \cdot 15 \cdot x^2 \cdot x^2 \cdot z^3 \cdot z} = \sqrt{45x^4z^4}$

Step3: Simplify the radical

$\sqrt{9 \cdot 5 \cdot (x^2)^2 \cdot (z^2)^2} = \sqrt{9} \cdot \sqrt{5} \cdot \sqrt{(x^2)^2} \cdot \sqrt{(z^2)^2} = 3x^2z^2\sqrt{5}$

Answer:

$3x^2z^2\sqrt{5}$