How do you simplify sqrt(5/3)?

1 Answer
George C.
Sep 18, 2017

sqrt(5/3) = sqrt(15)/3

Explanation:

Note that if b > 0 then:

sqrt(a/b) = sqrt(a)/sqrt(b)

The same is not true if a > 0 and b < 0.

Given to simplify:

sqrt(5/3)

The way I have seen most people address this kind of problem is to separate the square root then rationalise the denominator by multiplying both numerator and denominator by sqrt(3), so:

sqrt(5/3) = sqrt(5)/sqrt(3) = (sqrt(5)sqrt(3))/(sqrt(3)sqrt(3)) = sqrt(15)/3

Personally, I prefer to multiply the numerator and denominator by 3 first, in order to make the denominator into a perfect square, thus:

sqrt(5/3) = sqrt(15/3^2) = sqrt(15)/sqrt(3^2) = sqrt(15)/3

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