Question

8.4 add, subtract, and multiply radical expressions
score: 13.8/22 answered: 14/22
question 15
simplify. assume all variables are nonnegative.
(5\sqrt{6y})(3\sqrt{5y}) =
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Explanation:

Step1: Multiply the coefficients

Multiply 5 and 3: $5\times3 = 15$.

Step2: Multiply the radicands

Multiply $\sqrt{6y}$ and $\sqrt{5y}$ using the rule $\sqrt{a}\cdot\sqrt{b}=\sqrt{ab}$. So $\sqrt{6y}\cdot\sqrt{5y}=\sqrt{6y\times5y}=\sqrt{30y^{2}}$.

Step3: Simplify the radical

Since $y$ is non - negative, $\sqrt{30y^{2}} = y\sqrt{30}$.

Step4: Combine the results

Multiply the result from Step1 and Step3: $15\times y\sqrt{30}=15y\sqrt{30}$.

Answer:

$15y\sqrt{30}$