How do you simplify #sqrt(343/280)#?

1 Answer
Mar 21, 2017

Answer:

#sqrt(343/280) = (7sqrt10)/20#

Explanation:

First pull out as many perfect squares as possible:

#sqrt(343/280) = sqrt((color(red)7*color(red)7*7)/(color(blue)2*color(blue)2*2*7*5)) = color(red)7/color(blue)2sqrt(7/(2*7*5))#

Next, cancel out any terms left inside the radical and simplify.

#7/2sqrt(cancel7/(2*cancel7*5)) = 7/2sqrt(1/10) = 7/(2sqrt10)#

Now, multiply both the numerator and denominator by #sqrt10# to rationalize the denominator.

#7/(2sqrt10)*sqrt10/sqrt10 = (7sqrt10)/(2*10) = (7sqrt10)/20#

Final Answer