How do you simplify #sqrt8/(2sqrt7)#?

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Answer 1 · 2018-04-14T18:36:16

#sqrt14/7#

#sqrt8/(2sqrt7)#

#(sqrt(4 * 2))/(2sqrt7)#

#(sqrt4 * sqrt2)/(2sqrt7)#

#(2sqrt2)/(2sqrt7)#

Since both the numerator and denominator is multiplied by #2#, we can cancel #2#:
#(color(red)(cancel(2))sqrt2)/(color(red)(cancel(2))sqrt7)#

And what's left is:
#sqrt2/sqrt7#

If you need to simplify it further, you can rationalize the denominator by multiplying the whole expression by #sqrt7#:
#sqrt2/(sqrt7) * sqrt7/sqrt7#

Which becomes:
#sqrt14/7#

Hope this helps!