SOLUTION: What is radical50 plus radical 10? Please show steps :-)

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Question 887208: What is radical50 plus radical 10? Please show steps :-)
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
i believe you mean simplify the expression.

start with sqrt(50) + sqrt(10)

since 10 = 2 * 5 and 50 = 5 * 10 = 5 * 2 * 5, your expression becomes:

sqrt(5 * 2 * 5) + sqrt(2 * 5) which becomes:

sqrt(5^2 * 2) + sqrt(2 * 5) which becomes:

sqrt(5^2) * sqrt(2) + sqrt(2) * sqrt(5) which becomes:

5 * sqrt(2) + sqrt(2) * sqrt(5).

factor out the common term of sqrt(2) and you get:

sqrt(2) * (5 + sqrt(5)

confirm by evaluating sqrt(50) + sqrt(10) and comparing it to the evaluation of sqrt(2) * (5 + sqrt(5)) to see if you get the same answer from both.

sqrt(50) + sqrt(10) = 10.23334547

sqrt(2) * (5 + sqrt(5)) = 10.23334547

they're the same so the simplification problem is successful.