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Converting Radicals
Simplifying Radicals/division
Operations with Radicals
Radical Equations
miscellaneous
100

Rewrite in Exponential Form

1/sqrt(2x)

(2x)^-(1/2)

100

Simplify 

-5sqrt(448m^3n^4p^3

-40n^2mpsqrt(7mp

100

Simplify 

3sqrt(20)-2sqrt(12)+2sqrt(5)

8sqrt(5)-4sqrt3)

100

solve 

sqrt(5x-1)+4=11

x=10

100

Write the inverse function 

f(x)=sqrt(x)-5

f(x)^-1=(x+5)^2

200

rewrite in exponential form 

root(3)(3^5x^7y^4)

(3^5x^7y^4)^(1/3)

200

Simplify 

-7root(5)(-224m^4n^8)

14nroot(5)(7m^4n^3)

200

Simplify 

-root(3)(81)-2root(3)(40)-root(3)(3)+2root(3)5

-4root(3)(3)-2root(3)(5)

200

root(4)(3x+6)=-3

no solution

200

Determine if the functions are inverses 

f(x)=6x-15

g(x)=1/6x+5/2

yes

300

rewrite in radical form 

(4^2x^9y^15)^(1/4)

root(4)(4^2x^9y^15)

300

simplify 

sqrt((70p^10)/(2p^7)

psqrt(35p)

300

Simplify 

sqrt(2)(sqrt2+5)

2+5sqrt2

300

root(3)(x^2+5)=root(3)(x^2-4x+1)

x=-1

300

Determine if the functions are inverse functions

g(x)=root(3)(4x-12)

f(x)=1/4x^3-3

no

400

rewrite in radical form

1/(5y)^(-1/3)

root(3)5y

400

write in simplest radical form 

k^(13/3)/k

k^3root(3)k

400

Simplify 

(4sqrt(2)-3)(sqrt(2)-1)

11-7sqrt2

400

sqrt(8x)=x

x=0,8

400

determine the domain and range of the function 

f(x)=-sqrt(x+6)+5

Domain: [-6,infinty)

Range: (-infinity,5]

500

Rewrite in radical form 

(5x)^(-1/2)/y^(-1/4)

root(4)(y)/root(2)(5x)

500

Simplify 

root(3)7/root(3)56

=

1/2

500

Simplify 

-5sqrt3(2sqrt3+4a)

-30-20asqrt3

500

sqrt(2x+3)=x+2

v=-1

500

Rationalize the denominator 

(sqrt3-3sqrt5)/(2+sqrt5)

-2sqrt3+sqrt15+6sqrt5-15