Verified answer

You kind of have to work backwards...

9√⅓ ... the 9 came from taking out 3 and 3 from inside the radical (there was originally 81 inside, 81= 9*9, you pull the nine out).

Now we have √⅓ *81 (all inside the radical). which multiplies to √81/3, simplified to √27.

√27 = √9*√3. The square root of nine is equal to 3, so you pull that out of the radical. You are left with 3√3!

I know the explination is choppy, but it was hard to explain! I hope you understood. Good luck!

You need to remove the fraction from the radical. To do that multiply the 1/3 by 3/3 (multiplying by 1 [3/3] does not change the value). This gives you 9 sqrt 3/9 which simplifies to 9sqrt3/3.

y = 3x² - 3x - 2 3x² - 3x - 2 = 0 3x² - 3x = 2 3(x² - x) = 2 x² - x = 2/3 x² - x + a million/4 = 2/3 + a million/4 (x - a million/2)² = 8/12 + 3/12 (x - a million/2)² = 11/12 x - a million/2 = ?(11/12) x = a million/2 ± ?(11/12) ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

9√⅓

9 √(3/9)

9 √3/√9

(9/3)√3

I'll try to explain :

9srt(1/3). =

3x3 srt(1/3) =

3 srt(9 x 1/3) =

3 srt(9/3) =

3 srt(3)

9√⅓ = 9·(√1/√3) = 9·[(√1/√3)·(√3/√3)] = 9·[√3/3] = 3√3

I find my method a bit easier.

9√⅓ = √81 × √⅓

= √(81 × ⅓)

= √(81/3)

= √27

= √(9 × 3)

= √9 × √3

= 3√3

root[1/3] = 1/root[3] = root[3]/3 x 9 = ans