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

Answer 1

#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

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Answer 2

Jameson Allen

To simplify sqrt(343/280), we can simplify the fraction first. The greatest common divisor (GCD) of 343 and 280 is 7. Dividing both numbers by 7 gives us 49/40. Now, taking the square root of 49/40, we can simplify it further. The square root of 49 is 7, and the square root of 40 is 2√10. Therefore, sqrt(343/280) simplifies to 7/2√10.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.