How do you simplify #sqrt10-sqrt5#?

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Answer 1 · 2017-07-18T12:28:40

see a solution process below:

First, rewrite the radical on the left as:

#sqrt(2 * 5) - sqrt(5)#

Next, use this rule for radicals to rewrite the term on the left again:

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

#sqrt(color(red)(2) * color(blue)(5)) - sqrt(5) => sqrt(color(red)(2))sqrt(color(blue)(5)) - sqrt(5)#

Next, factor out the common terms:

#sqrt(2)sqrt(5) - sqrt(5) => sqrt(2)sqrt(5) - 1sqrt(5) =>#

#(sqrt(2) - 1)sqrt(5)#