What is #4sqrt42 + 2sqrt28 - sqrt7#?

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Answer 1 · 2018-03-09T20:18:46

#=sqrt7(4sqrt6+1)#

Write each of the radicands as a product of the factors:

#4sqrt42+2sqrt28-sqrt7#

#=4sqrt(6xx7) +2sqrt(4xx7) -sqrt7#

Split the roots into separate roots.

#=4sqrt6sqrt7 +sqrt4 sqrt7-sqrt7#

#=4sqrt6sqrt7 + 2sqrt7-sqrt7#

Take out the common factor of #sqrt7# from each term

#=sqrt7(4sqrt6 +2-1)#

#=sqrt7(4sqrt6+1)#

You cannot simplify further without a calculator.