Question

simplify.
multiply and remove all perfect squares from inside the square roots. assume ( z ) is positive.
( 5sqrt{14z^2} cdot 4sqrt{21z^3} = square )

Explanation:

Step1: Multiply coefficients and radicals

$5 \cdot 4 \cdot \sqrt{14z^2 \cdot 21z^3}$

Step2: Simplify coefficients and radicand

$20 \cdot \sqrt{294z^{2+3}} = 20\sqrt{294z^5}$

Step3: Factor radicand into perfect squares

$20\sqrt{49 \cdot 6 \cdot z^4 \cdot z} = 20\sqrt{49z^4 \cdot 6z}$

Step4: Extract perfect square roots

$20 \cdot 7z^2 \cdot \sqrt{6z}$

Step5: Multiply remaining coefficients

$20 \cdot 7z^2\sqrt{6z} = 140z^2\sqrt{6z}$

Answer:

$140z^2\sqrt{6z}$