How do you simplify #sqrt7( sqrt35 + sqrt 7)#?

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Answer 1 · 2017-08-08T03:13:08

See a solution process below:

First, multiply each term within the parenthesis by the term outside the parenthesis:

#color(red)(sqrt(7))(sqrt(35) + sqrt(7)) =>#

#(color(red)(sqrt(7)) xx sqrt(35)) + (color(red)(sqrt(7)) xx sqrt(7)) =>#

#(color(red)(sqrt(7)) xx sqrt(35)) + 7#

Next, rewrite the term on the left using this rule of radicals:

#sqrt(color(red)(a)) * sqrt(color(blue)(b)) = sqrt(color(red)(a) * color(blue)(b))#

#(color(red)(sqrt(7)) xx color(blue)(sqrt(35))) + 7 =>#

#sqrt(color(red)(7) xx color(blue)(35)) + 7 =>#

#sqrt(color(red)(7) xx color(blue)(7 xx 5)) + 7 =>#

#sqrt(color(red)(49) xx color(blue)(5)) + 7 =>#

#(sqrt(color(red)(49)) xx sqrt(color(blue)(5))) + 7 =>#

#7sqrt(color(blue)(5)) + 7#