Question

8.4 add, subtract, and multiply radical expressions
score: 16.8/22 answered: 17/22
question 18
simplify. assume all variables are nonnegative.
$(3sqrt{2y^{13}})(4sqrt{7y^{4}})=$
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Explanation:

Step1: Multiply the coefficients

Multiply 3 and 4. $3\times4 = 12$.

Step2: Multiply the radicands

Multiply $2y^{13}$ and $7y^{4}$. Using the rule $a^m\times a^n=a^{m + n}$ for exponents and multiplication of numbers, we have $(2y^{13})\times(7y^{4})=2\times7\times y^{13 + 4}=14y^{17}$.

Step3: Combine the results

The product is $12\sqrt{14y^{17}}$. Then, simplify $\sqrt{y^{17}}=\sqrt{y^{16}\times y}=y^{8}\sqrt{y}$. So the final - simplified form is $12y^{8}\sqrt{14y}$.

Answer:

$12y^{8}\sqrt{14y}$