First, note that radical 4 is 2. So 3xradical 4 is just 6, Now we have 6+2 radical 3. You can't do much with this except factor out a 2 if you want 2(3+Radical 3)
If we factor 60, we get 60 = 2 * 2 * 3 * 5 So sqrt ( 60 ) = sqrt (2 * 2 * 3 * 5) = sqrt (2 * 2) * sqrt (3 * 5) = 4 * sqrt( 15 ) ____________________________________________________________ actually if you do by just using the simpler way you should get 2 radical 15 since , 60 has the closest perfect square of 4 and non perfect of 15 this is how you should solve radical 60 = radical 4 times radical 15 radical 60 = simplify the 4 to 2 and leave radical 15 So , radical 60 = 2 radical 15 not what is above .
3
12(radical "3")
2
radical(48)/radical(3) = radical(48/3) = radical(16) = 4 Technically, radical(16) is +4 OR -4 but in such questions often only the principal root is required.
First, note that radical 4 is 2. So 3xradical 4 is just 6, Now we have 6+2 radical 3. You can't do much with this except factor out a 2 if you want 2(3+Radical 3)
4√3 + 7√3 = (4 + 7)(√3) = 11√3
If we read this carefully, what you're asking for is (4 of something) minus (1 of the same thing). The result is 3 of them . . . 3 radical 6.
The square root of 48 in radical form is 4√3.
Start by finding a common denominator. If the radical includes the entire fraction (3/4 for the first part), the common denominator would be square root of 12.
To simplify the expression radical 6 minus 4 radical 6, we first combine like terms. Since both terms have the same radical part (radical 6), we can subtract the coefficients in front of the radicals. This gives us -3 radical 6 as the simplified answer.
2√20 - 3√7 - 2√5 + 4√63 = 2√(4 x 5) - 3√7 - 2√5 + 4√(9 x 7) = 4√5 - 2√5 - 3√7 + 12√7 = 2√5 + 9√7
4 x2
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)
-3*radical(2)*radical(50) = -3*radical(2*50) = -3*radical(100) = -3*10 = -30
rad 12 - 3 rad 3rad 12 = rad(4*3) = rad (4) * rad(3) = 2 rad 32 rad 3 - 3 rad 3= - rad 3