Like this. Factor inside the radical.
3sqrt(2^2*2^2 *5)
as you can see....4 *4 = 16 * 5 = 80, so you can bring both 2,s out and multiply them against the 3
2*2*3sqrt(5)
= 12sqrt(5)
simplified
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2*sqrt(75) = 2*sqrt(25*3) = 2*sqrt(25)*sqrt(3) = 2*5*sqrt(3) = 10*sqrt(3)
3 sqrt (3)Put the radical where the "sqrt" is with the second 3 inside.
In order to work with radicals (adding or subtracting) they have to have the same radical expression. ex: 2 rad 3 + 4 rad 3 = 6 rad 3. If it helps, change the similar radicals to a variable. 2 rad 3 + 4 rad 3 2 x + 4 x = 6x and then substitute your radical back in for the variable. 6 rad 3 ---- rad 12 - 3 rad 3 Let's simplify radical 12. First, factor 12 into a perfect square, and a not perfect square.) Hint: we want it to be radical 3 to work with it... 3 times what is 12? rad 12 = sqrt(12) = sqrt(4*3) sqrt(4*3) = sqrt(4)*sqrt(3) sqrt(4) is just 2! We bring this to the "outside" of the radical. sqrt(4)*sqrt(3) = 2 sqrt(3) or 2 rad 3 rad 12 - 3 rad 3 2 rad 3 - 3 rad 3 (or 2x - 3x if it helps) We're left with: -1 rad 3, or just - rad 3 (negative radical 3)
sqrt(80/45) = sqrt(16/9) = sqrt(16)/sqrt(9) = 4/3 sqrt(80/45) = sqrt(16/9) = sqrt(16)/sqrt(9) = 4/3 sqrt(80/45) = sqrt(16/9) = sqrt(16)/sqrt(9) = 4/3 sqrt(80/45) = sqrt(16/9) = sqrt(16)/sqrt(9) = 4/3
sqrt(363) = sqrt(121*3) = sqrt(121)*sqrt(3) = 11*sqrt(3)