How do you simplify sqrt(350)?

2 Answers
Jan 7, 2016

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

5timessqrt(14)

Explanation:

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

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

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