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

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Answer 1 · 2017-03-21T03:40:06

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

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

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