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].
