Answer:
Simplified radical form is [tex]16\sqrt{6}[/tex]
Step-by-step explanation:
In this problem we have the sum of two radical expressions. First step is to rewrite the radical using factorization process. Numbers 54 and 24 can be written as the products of square and non-square numbers.
[tex]54 = 9 * 6 = 3^{2} *6\\24 = 4* 6 = 2^{2} *6[/tex]
After that, we can replace the numbers in the radical expression, and we can simplify them. Square numbers can be simplified with the radical. Then, we can expand the products.
[tex]2\sqrt{54} + 5\sqrt{24}\\2\sqrt{6*9} + 5\sqrt{4*6}\\2\sqrt{3^{2} * 6} + 5\sqrt{2^{2}*6}\\2\sqrt{3^{2}}*\sqrt{6} + 5\sqrt{2^{2}}*\sqrt{6}\\2*3*\sqrt{6} + 5*2*\sqrt{6}\\6\sqrt{6} + 10\sqrt{6}[/tex]
Now, we can take the radical as common term and add the numbers.
[tex]6\sqrt{6} + 10\sqrt{6}\\\sqrt{6}* (6+10)\\16\sqrt{6}[/tex]
Finally, Simplified radical form is [tex]16\sqrt{6}[/tex]
