Answer:
![5\sqrt[]{6}](https://tex.z-dn.net/?f=5%5Csqrt%5B%5D%7B6%7D)
Step-by-step explanation:
![\sqrt[]{54}+\sqrt[]{24}](https://tex.z-dn.net/?f=%5Csqrt%5B%5D%7B54%7D%2B%5Csqrt%5B%5D%7B24%7D)
We can rewrite 54 as 6*9 and 9 can be rewritten as
.
24 can be rewritten as 3*8 and 8 can be rewritten as
or 
I'm doing this because that way I can easily take those numbers out of the square (2) root.
Let's rewrite our square roots.
![\sqrt[]{6*3^2}+\sqrt[]{3*2^2*2}](https://tex.z-dn.net/?f=%5Csqrt%5B%5D%7B6%2A3%5E2%7D%2B%5Csqrt%5B%5D%7B3%2A2%5E2%2A2%7D)
3 cancels the square in the first square root, and same does 2 squared in the second square root.
![3\sqrt[]{6}+2\sqrt[]{3*2}](https://tex.z-dn.net/?f=3%5Csqrt%5B%5D%7B6%7D%2B2%5Csqrt%5B%5D%7B3%2A2%7D)
Solve;
![3\sqrt[]{6}+2\sqrt[]{6}](https://tex.z-dn.net/?f=3%5Csqrt%5B%5D%7B6%7D%2B2%5Csqrt%5B%5D%7B6%7D)
When you have square roots with equal value inside, you can add the numbers outside of it.
![3+2(\sqrt[]{6})](https://tex.z-dn.net/?f=3%2B2%28%5Csqrt%5B%5D%7B6%7D%29)
![5\sqrt[]{6}](https://tex.z-dn.net/?f=5%5Csqrt%5B%5D%7B6%7D)