What is #sqrt5 - sqrt20#?

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Answer 1 · 2018-03-19T17:32:29

#=-sqrt5#

Both these numbers are irrational, so there is no exact answer, but we can change what is given..

#sqrt5 -sqrt20#

#sqrt5 - sqrt(4xx5)#

#=sqrt5 -2sqrt5#

#=-sqrt5#

Answer 2 · 2018-03-19T17:34:51

By simplifying and then grouping, I found the answer is #-sqrt(5)#

I first simplified the #sqrt(20)# as shown below:

#sqrt(20)=sqrt(4*5)=sqrt(4)*sqrt(5)=2sqrt(5)#

Now that we have two #sqrt(5)# terms, we can write it as factors:

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

Now, solve for the terms in the parentheses and you have your answer:

#sqrt(5)(1-2)=sqrt(5)(-1)=color(red)(-sqrt(5))#