How do you simplify #sqrt(350)#?

2 Answers
Jan 7, 2016

Answer:

#5sqrt14#

Explanation:

search for the factors of #350# looking for one that is a perfect square.

In this case # 25 xx 14 #

#25# being the perfect square.

# sqrt350 = sqrt ( 25 xx 14 ) #

now #sqrt(ab) = sqrta xx sqrtb # (so long as at least one of #a# and #b# is not negative)

#rArr sqrt(25 xx 14) = sqrt25 xx sqrt14 #

The factors of #14# do not contain any square numbers apart from #1# and so #sqrt14# cannot be simplified any further.

#rArr sqrt350 = 5sqrt14#

Jan 7, 2016

Answer:

#5timessqrt(14)#

Explanation:

#350=35times10=7times5times2times5=2times5^2times7#

#sqrt(350)=sqrt(2times5^2times7)=sqrt(5^2)timessqrt(2times7)=#

#5timessqrt(2times7)=5timessqrt(14)#