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Simplify (sqrt(5) + sqrt(45) + sqrt(125) \(+ \sqrt{80}\))^2

 Jan 24, 2022
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First we simplify the radicals in the parenthesis. 

\(\sqrt{5} = \sqrt{5}\)

\(\sqrt{45} = 3\sqrt{5}\)

\(\sqrt{125} = 5\sqrt{5}\)

\(\sqrt{80}=4\sqrt{5}\)

 

Since we are adding up the radicals, our new expression is:

\((\sqrt{5} + 3\sqrt{5} +5\sqrt{5}+ 4\sqrt{5})^2\)

 

Simplifying we get:

\((13\sqrt{5})^2\)

 

This simplifies to:

845 which is the answer.

 

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 Jan 24, 2022

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