How do you simplify #5/sqrt10#?

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Answer 1 · 2016-10-04T22:34:29

#sqrt10/2#

You have to follow a process called rationalizing when you have a denominator that is an irrational number.

In this process you multiply the numerator and denominator by the irrational number that is in the denominator.

#sqrt10/sqrt10#

This is the same as multiplying by 1, so the look of the ratio but it is still equivalent.

#sqrt10/sqrt10# is the same as 1.

#5/sqrt10*sqrt10/sqrt10=(5sqrt10)/sqrt100=(5sqrt10)/10=(cancel5sqrt10)/(cancel5*2)=sqrt10/2#

Answer 2 · 2016-10-04T22:38:01

Always multiply by the surd you want to eliminate (#sqrt(10)#)

#5/sqrt(10)#=#5/sqrt(10) * sqrt(10)/sqrt(10)#
# =(5*sqrt(10) ) / 10#
# =sqrt(10) / 2#
# =sqrt(2*5) / 2#
# =1/2sqrt(10)#
# =1/2 sqrt(2) sqrt(5)#