i need to simplify the square root of 1/5 how would i go about doing this?

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- May 3rd 2007, 06:48 PMtrippymsimplify radical
i need to simplify the square root of 1/5 how would i go about doing this?

- May 3rd 2007, 06:52 PMJhevon
- May 3rd 2007, 06:52 PMecMathGeek
sqrt(1/5) = sqrt(1)/sqrt(5) = 1/sqrt(5)

However, we usually don't want radicals on the denominator, so we need to "rationalize" the denominator by multiplying both the numerator and denominator by sqrt(5):

1/sqrt(5) * sqrt(5)/sqrt(5)

= sqrt(5)/[sqrt(5)*sqrt(5)]

= sqrt(5)/[sqrt(25)]

= sqrt(5)/5 - May 3rd 2007, 06:59 PMtrippym
thanks a lot that helped one other question

i have the problem square root of 3/2 multiplied by the square root of 5/6 for my answer i got the square root of 180 over 12 is that right? - May 3rd 2007, 07:12 PMJhevon
the products of square roots are the square roots of the products, we can see this more explicitly if we represent squareroots as powers. So,

sqrt(3/2) * sqrt(5/6) = sqrt[(3/2)*(5/6)]

.............................= sqrt(15/12)

.............................= sqrt(15)/sqrt(12)

.............................= sqrt(5*3)/sqrt(3*4)

.............................= [sqrt(3)*sqrt(5)]/[sqrt(3)*sqrt(4)]

.............................= sqrt(5)/2

EDIT: Just in case you were wondering, sqrt(180)/12 was correct, however, it was not simplified

sqrt(180)/12 = sqrt(36*5)/12

..................= sqrt(36)*sqrt(5)/12

..................= 6sqrt(5)/12

..................= sqrt(5)/2