Radical Functions & Equations — Drills
Radical Functions & Equations has 6 drill skills. Each one generates fresh questions every time, with a hint and full worked steps, so you can keep practising a single skill until it settles.
What these drills cover
These questions use 5 ideas from the course. Follow any of them for a definition, where it is taught, and what it leads to.
- Isolate — Get the variable alone on one side.
- Square root — For k ≥ 0, √k is the nonnegative number whose square is k.
- Radical — The √x symbol, and the expression under it.
- Roots — The x values where y = 0.
- Rational exponent — x1/2 = √x and xm/n = √[n]xm.
Solving
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Solve √x+12=4.
Worked answer
4
x+12=16
x=4
x=4
Problem 2
Solve √x+6=3.
Worked answer
3
x+6=9
x=3
x=3
Isolate
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Solve √x+8=14.
Worked answer
36
√x=6
x=36
Problem 2
Solve √x+1=6.
Worked answer
25
√x=5
x=25
Exponents
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Evaluate 813/4.
Worked answer
27
√[4]81=3
33=27
Problem 2
Evaluate 642/6.
Worked answer
4
√[6]64=2
22=4
Start
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
At what x does y=√x-7 begin?
Worked answer
7
x-7 ≥ 0
x ≥ 7
Problem 2
At what x does y=√x-10 begin?
Worked answer
10
x-10 ≥ 0
x ≥ 10
Cubes
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Solve √[3]x=-6.
Worked answer
-216
x=-63
=-216
Problem 2
Solve √[3]x=-2.
Worked answer
-8
x=-23
=-8
Extraneous
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Solve √x+42=x. Give the only valid answer.
Worked answer
7
x+42=x2
x2-x-42=0 gives x=7 or x=-6
x=-6 fails: a square root is never negative
Problem 2
Solve √x+2=x. Give the only valid answer.
Worked answer
2
x+2=x2
x2-x-2=0 gives x=2 or x=-1
x=-1 fails: a square root is never negative