To solve the given expression [tex]\((4 \sqrt{3})(5 \sqrt{13}) = w \sqrt{z}\)[/tex] and find the value of [tex]\(w + z\)[/tex], follow these steps:
1. Simplify the Expression: Start by multiplying the given terms:
[tex]\[
(4 \sqrt{3})(5 \sqrt{13})
\][/tex]
2. Multiply the Coefficients: First, multiply the coefficients outside the square roots:
[tex]\[
4 \times 5 = 20
\][/tex]
3. Multiply the Radicands: Next, multiply the numbers inside the square roots:
[tex]\[
\sqrt{3} \times \sqrt{13} = \sqrt{3 \times 13} = \sqrt{39}
\][/tex]
4. Combine the Results: Combine the results into a single expression:
[tex]\[
(4 \sqrt{3})(5 \sqrt{13}) = 20 \sqrt{39}
\][/tex]
5. Identify [tex]\(w\)[/tex] and [tex]\(z\)[/tex]: From the simplified expression [tex]\(20 \sqrt{39}\)[/tex], we observe:
[tex]\[
w = 20 \quad \text{and} \quad z = 39
\][/tex]
6. Calculate [tex]\(w + z\)[/tex]: Now, add [tex]\(w\)[/tex] and [tex]\(z\)[/tex] together:
[tex]\[
w + z = 20 + 39 = 59
\][/tex]
Therefore, the value of [tex]\(w + z\)[/tex] is [tex]\(59\)[/tex].
