SME
Grade 11 Math · Algebra 2
Radical functions and equations
Use this for “Solve √(3x + 4) = 5.”
Chart
x = 7
c = 5
a = 3
b = 4
This is an example. Type your own values to start a new problem.
x
+
=
c
a
x
+
b
=
c
2
x
Solution
calculated
Formulas
a
×
x
+
b
=
c
2
3
×
7
+
4
=
5
2
Assumptions
•
Square both sides to undo the root: ax + b = c².
•
A square root is never negative, so c must be 0 or more.
•
Check the answer in the first equation.
Step-by-step
WE KNOW
a = 3, b = 4, c = 5
FIND
solution (x)
Step 1 · Find solution (x)
Use a × x + b = c²
Square
both
sides,
take
b
from
both
sides,
then
divide
by
a
.
x
=
c
2
−
b
a
x
=
5
2
− 4
3
x
=
25 − 4
3
x
=
21
3
x
=
7
Check
Put the numbers back in. Both sides should match.
√
3 × 7 + 4
=
5
✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.
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Graph a cube root function
Use this for “Graph y = 2∛(x + 1) − 3: its center, and y at x = 7” or “Find x where y = 5.”
Rational exponents
Use this for “Evaluate 82/3”, “Graph y = 2x−1/2” or “Solve x3/2 = 27.”