Answer :

To solve the expression [tex]\((4 \sqrt{2})(3 \sqrt{13}) = w \sqrt{z}\)[/tex] and find the value of [tex]\(w + z\)[/tex], we need to follow these steps:

1. Simplify the product of the constants outside the square roots:
[tex]\[ 4 \times 3 = 12 \][/tex]
This will be part of the constant [tex]\(w\)[/tex].

2. Simplify the product of the square roots:
[tex]\[ \sqrt{2} \times \sqrt{13} = \sqrt{2 \times 13} = \sqrt{26} \][/tex]
This will be under the square root, which corresponds to [tex]\(z\)[/tex].

3. Combine the results:
[tex]\[ (4 \sqrt{2})(3 \sqrt{13}) = 12 \sqrt{26} \][/tex]
Thus, by comparing this with [tex]\(w \sqrt{z}\)[/tex], we identify [tex]\(w = 12\)[/tex] and [tex]\(z = 26\)[/tex].

4. Calculate [tex]\(w + z\)[/tex]:
[tex]\[ w + z = 12 + 26 = 38 \][/tex]

So, the value of [tex]\(w + z\)[/tex] is [tex]\(38\)[/tex].