Jeopardy!!! (one more time)

Numbers

100

root(5)(-32)

-2

200

root(4)(81/256)

3/4

300

root(4)(48cdot27)

6

400

root(3)(-25)cdotroot(6)(25)

-5

500

root(5)(-243/1024)cdot root(3)(-4 17/27)

5/4

С2

100

sqrt20\cdot\sqrt5

10

200

\root(3)(54)/\root(3)(2)

3

300

\root(3)(5a^2b^2)cdotroot(3)(5^2a^4b^4)

5a^2b^2

400

root(4)(6+2sqrt5)cdotroot(4)(6-2sqrt5)

2

500

sqrtx-5root(4)(x)+6=0

x₁=16, x₂=81

С3

100

sqrt245

7sqrt5

200

(root(3)(3a))^9

27a³

300

(2root(3)(-3a^2))^5

864a^3root(3)(-9a)

400

sqrt(50)-root(3)(3)-6sqrt2+root(3)(24)+sqrt(8)

sqrt2+root(3)3

500

root(4)(2x)+root(4)(32x)+root(4)(162x)=6

x=1/2

С4

100

\sqrt108

6\sqrt3

200

(\sqrt3)^4

9

300

\root(12)(a^2b^3):\root(12)(ab^4)

root(12)(a/b)

400

root(3)(8-sqrt37)cdotroot(3)(8+sqrt37)

3

500

You got very lucky!

YEAAAAAH

С5

100

root(4)(486)

3root(4)(6)

200

sqrt(root(3)(x))

root(6)x

300

 (5acdotroot(5)(6a))^3 

125a^3root(5)(216a^3)

400

(root(3)m-2root(3)n)^2

root(3)(m^2)-4root(3)(mn)+4root(3)(n^2)

500

root(3)x-2root(6)x+1=0

x₁=x₂=1