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.