What is the simples form of the the following expression? 2 square root 18 + 3 square root 2 + square root 162

18 sqrt (2)

Step-by-step explanation:

Simplify the following:

2 sqrt (18) + 3 sqrt (2) + sqrt (162)

sqrt (18) = sqrt (2*3^2) = 3 sqrt (2):

2*3 sqrt (2) + 3 sqrt (2) + sqrt (162)

2*3 = 6:

6 sqrt (2) + 3 sqrt (2) + sqrt (162)

sqrt (162) = sqrt (2*3^4) = 3^2 sqrt (2):

6 sqrt (2) + 3 sqrt (2) + 3^2 sqrt (2)

3^2 = 9:

6 sqrt (2) + 3 sqrt (2) + 9 sqrt (2)

Add like terms. 6 sqrt (2) + 3 sqrt (2) + 9 sqrt (2) = 18 sqrt (2):

Answer: 18 sqrt (2)