Answer:
[tex]5\sqrt[]{6}[/tex]
Step-by-step explanation:
[tex]\sqrt[]{54}+\sqrt[]{24}[/tex]
We can rewrite 54 as 6*9 and 9 can be rewritten as [tex]3^2[/tex].
24 can be rewritten as 3*8 and 8 can be rewritten as [tex]2^3[/tex] or [tex]2^2*2[/tex]
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.
[tex]\sqrt[]{6*3^2}+\sqrt[]{3*2^2*2}[/tex]
3 cancels the square in the first square root, and same does 2 squared in the second square root.
[tex]3\sqrt[]{6}+2\sqrt[]{3*2}[/tex]
Solve;
[tex]3\sqrt[]{6}+2\sqrt[]{6}[/tex]
When you have square roots with equal value inside, you can add the numbers outside of it.
[tex]3+2(\sqrt[]{6})[/tex]
[tex]5\sqrt[]{6}[/tex]
