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3 years ago

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

Mathematics

1 answer:

Nataliya [291]3 years ago

6 0

Answer:

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)

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