Let's solve the expression step-by-step:
1. Start with the given expression:
[tex]\[
4 \sqrt{13} - 6 \sqrt{13} + 10 \sqrt{13}
\][/tex]
2. Notice that all terms involve [tex]\(\sqrt{13}\)[/tex]. We can combine these like terms by factoring out [tex]\(\sqrt{13}\)[/tex].
3. Combine the coefficients of [tex]\(\sqrt{13}\)[/tex]:
[tex]\[
4 - 6 + 10 = 8
\][/tex]
4. Now we can write the expression as:
[tex]\[
8 \sqrt{13}
\][/tex]
This is the simplified form of the expression.
When calculated, the numerical value of:
[tex]\[
8 \sqrt{13} \approx 28.844410203711917
\][/tex]
Thus, the simplified expression [tex]\(8 \sqrt{13}\)[/tex] numerically equals approximately 28.844410203711917.
