Answer:
[tex]3\sqrt{5}\:-\:3\sqrt{11}+22-9\sqrt{10}[/tex]
Step-by-step explanation:
Given
[tex]3\sqrt{5}\:-\:3\sqrt{11}+2\sqrt{121}-3\sqrt{90}[/tex]
Required
Simplify the expression
[tex]3\sqrt{5}\:-\:3\sqrt{11}+2\sqrt{121}-3\sqrt{90}[/tex]
Express the square root of 121 as 11
[tex]3\sqrt{5}\:-\:3\sqrt{11}+2 * 11-3\sqrt{90}[/tex]
[tex]3\sqrt{5}\:-\:3\sqrt{11}+22-3\sqrt{90}[/tex]
Express 90 as 9 * 10
[tex]3\sqrt{5}\:-\:3\sqrt{11}+22-3\sqrt{9 * 10}[/tex]
Split the surd to 2
[tex]3\sqrt{5}\:-\:3\sqrt{11}+22-3\sqrt{9} * \sqrt10}[/tex]
Express the square root of 9 as 3
[tex]3\sqrt{5}\:-\:3\sqrt{11}+22-3 * 3 * \sqrt10}[/tex]
[tex]3\sqrt{5}\:-\:3\sqrt{11}+22-9 * \sqrt10}[/tex]
[tex]3\sqrt{5}\:-\:3\sqrt{11}+22-9\sqrt{10}[/tex]
Hence, the result of the expression is
[tex]3\sqrt{5}\:-\:3\sqrt{11}+22-9\sqrt{10}[/tex]
