Question

Simplify the radical expression completely LaTeX: 3\sqrt{5}\:-\:3\sqrt{11}+2\sqrt{121}-3\sqrt{90}3 5 − 3 11 + 2 121 − 3 90 A. LaTeX: 5\sqrt{31}5 31 B. LaTeX: 3\sqrt{16}+\sqrt{15}-\:43 16 + 15 − 4 C. LaTeX: 3\sqrt{5}-3\sqrt{11}+22\:-9\sqrt{10}3 5 − 3 11 + 22 − 9 10 D. Cannot be simplified further Group of answer choices

Answer 1

`3√(5)\:-\:3√(11)+22-9√(10)`

Explanation:

Given

`3√(5)\:-\:3√(11)+2√(121)-3√(90)`

Required

Simplify the expression

`3√(5)\:-\:3√(11)+2√(121)-3√(90)`

Express the square root of 121 as 11

`3√(5)\:-\:3√(11)+2 * 11-3√(90)`

`3√(5)\:-\:3√(11)+22-3√(90)`

Express 90 as 9 * 10

`3√(5)\:-\:3√(11)+22-3√(9 * 10)`

Split the surd to 2

`3√(5)\:-\:3√(11)+22-3√(9) * \sqrt10}`

Express the square root of 9 as 3

`3√(5)\:-\:3√(11)+22-3 * 3 * \sqrt10}`

`3√(5)\:-\:3√(11)+22-9 * \sqrt10}`

`3√(5)\:-\:3√(11)+22-9√(10)`

Hence, the result of the expression is

`3√(5)\:-\:3√(11)+22-9√(10)`