Question

8.4 add, subtract, and multiply radical expressions
score: 15.8/22 answered: 16/22
question 17
simplify. assume all variables are nonnegative.
(3√(3z^7))(5√(5z^10)) =
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Explanation:

Step1: Multiply the coefficients

Multiply 3 and 5.
$3\times5 = 15$

Step2: Multiply the radicands

Multiply $\sqrt{3z^{7}}$ and $\sqrt{5z^{10}}$. According to the rule $\sqrt{a}\cdot\sqrt{b}=\sqrt{ab}$, we have $\sqrt{3z^{7}\cdot5z^{10}}=\sqrt{15z^{7 + 10}}=\sqrt{15z^{17}}$.

Step3: Simplify the radicand

Rewrite $z^{17}$ as $z^{16}\cdot z$. Then $\sqrt{15z^{17}}=\sqrt{15z^{16}\cdot z}=z^{8}\sqrt{15z}$.

Step4: Combine the results

Multiply the result from Step1 and Step3.
$15\times z^{8}\sqrt{15z}=15z^{8}\sqrt{15z}$

Answer:

$15z^{8}\sqrt{15z}$