# Thread: simplify radical

1. ## simplify radical

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

2. Originally Posted by trippym
i need to simplify the square root of 1/5 how would i go about doing this?
well, the sqrt(1/5) doesn't get much simpler.

sqrt(1/5) = sqrt(1)/sqrt(5) = 1/sqrt(5) or sqrt(5)/5 if we want to rationalize the denominator

3. Originally Posted by trippym
i need to simplify the square root of 1/5 how would i go about doing this?
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

4. 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?

5. Originally Posted by trippym
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?
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