Question

simplify. multiply and remove all perfect squares from inside the square roots. assume z is positive. \\(sqrt{z} cdot sqrt{30z^2} cdot sqrt{35z^3} = \\) \\(square\\)

Explanation:

Step1: Combine square roots

$\sqrt{z \cdot 30z^2 \cdot 35z^3}$

Step2: Multiply constants and z terms

$\sqrt{(30 \cdot 35) \cdot (z \cdot z^2 \cdot z^3)} = \sqrt{1050 \cdot z^{6}}$

Step3: Factor out perfect squares

$\sqrt{25 \cdot 42 \cdot z^{6}} = \sqrt{25} \cdot \sqrt{z^6} \cdot \sqrt{42}$

Step4: Simplify perfect square roots

$5 \cdot z^3 \cdot \sqrt{42}$

Answer:

$5z^3\sqrt{42}$