How do you find the square root of the fraction 64/100?

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Answer 1 · 2015-09-04T18:08:40

Have a look:

You can write:
#sqrt(64/100)=sqrt(64)/sqrt(100)=# and solve the two (exact) roots separately!
So you get:
#8/10=4/5#

Answer 2 · 2015-09-04T19:09:28

#64/100 = 16/25 = (4*4)/(5*5) = (4/5)*(4/5) = (4/5)^2#

So #sqrt(64/100) = sqrt((4/5)^2) = 4/5#

In general, if #a >= 0# then #sqrt(a^2) = a#

Also, if #b > 0#, then #sqrt(a/b) = sqrt(a)/sqrt(b)#, though we did not have to use that this time.