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

Answer:

$3\sqrt{5}\:-\:3\sqrt{11}+22-9\sqrt{10}$

Step-by-step explanation:

Given

$3\sqrt{5}\:-\:3\sqrt{11}+2\sqrt{121}-3\sqrt{90}$

Required

Simplify the expression

$3\sqrt{5}\:-\:3\sqrt{11}+2\sqrt{121}-3\sqrt{90}$

Express the square root of 121 as 11

$3\sqrt{5}\:-\:3\sqrt{11}+2 * 11-3\sqrt{90}$

$3\sqrt{5}\:-\:3\sqrt{11}+22-3\sqrt{90}$

Express 90 as 9 * 10

$3\sqrt{5}\:-\:3\sqrt{11}+22-3\sqrt{9 * 10}$

Split the surd to 2

$3\sqrt{5}\:-\:3\sqrt{11}+22-3\sqrt{9} * \sqrt10}$

Express the square root of 9 as 3

$3\sqrt{5}\:-\:3\sqrt{11}+22-3 * 3 * \sqrt10}$

$3\sqrt{5}\:-\:3\sqrt{11}+22-9 * \sqrt10}$

$3\sqrt{5}\:-\:3\sqrt{11}+22-9\sqrt{10}$

Hence, the result of the expression is

$3\sqrt{5}\:-\:3\sqrt{11}+22-9\sqrt{10}$