To solve the expression [tex]\((3 \sqrt{7})(2 \sqrt{5})=w \sqrt{z}\)[/tex] and find the value of [tex]\(w + z\)[/tex], let's break the problem down step-by-step.
1. Understand the given terms:
[tex]\( \text{term1} = 3 \sqrt{7} \)[/tex]
[tex]\( \text{term2} = 2 \sqrt{5} \)[/tex]
2. Multiply the given terms:
[tex]\[
3 \sqrt{7} \times 2 \sqrt{5}
\][/tex]
3. Use the property of multiplication of radicals:
[tex]\[
(3 \cdot 2) \cdot (\sqrt{7} \cdot \sqrt{5})
\][/tex]
[tex]\[
3 \times 2 = 6
\][/tex]
[tex]\[
\sqrt{7} \times \sqrt{5} = \sqrt{7 \times 5} = \sqrt{35}
\][/tex]
4. Combine the constants with the radicals:
[tex]\[
6 \sqrt{35}
\][/tex]
So, we see [tex]\(w = 6\)[/tex] and [tex]\(z = 35\)[/tex] in the expression [tex]\(6 \sqrt{35}\)[/tex].
5. Add [tex]\(w\)[/tex] and [tex]\(z\)[/tex] together:
[tex]\[
w + z = 6 + 35
\][/tex]
6. That results in:
[tex]\[
w + z = 41
\][/tex]
So the value of [tex]\(w + z\)[/tex] is [tex]\(\boxed{41}\)[/tex].
