Radical equations are equations that have variables stunk inside a radical. We will show you how to solve this type of equations in this lesson.

Lessons

3-step approach for solving radical equations:

1) Isolate the “square root” term.

2) i. Square both sides of the equation to get rid of the “square root”.

ii. (optional) If the resulting equation still has a “square root” term, repeat steps 1 and 2.

3) Solve the equation, and REMEMBER to substitute answers back into the original equation to identify any EXTRANEOUS ROOTS,
• 1.
Solving Radical Equations Involving One Square Root Term
Solve:
a)
$3\sqrt {x - 2} + x = 0$
(hint: no solutions)

b)
$x - 2 = 2\sqrt {x + 1}$
(hint: one solutions)

c)
$x + \sqrt {2{x^2} - 7} = 3$
(hint: two solutions)

d)
$\sqrt {x + 9} - 10 = - 8$
(hint: one solutions)

• 2.
Solving Radical Equations Involving More than One Square Root Term
Solve:
a)
$\sqrt{3x+4}-\sqrt{x+1}=3$
(hint: one solutions)

b)
$\sqrt{x-2}+3=\sqrt{2x+5}$
(hint: two solutions)

c)
$\sqrt{x-4}+\sqrt{x}=4$
(hint: one solutions)

d)
$\sqrt{5x+20}=\sqrt{x+8}+\sqrt{x+3}$
(hint: two solutions)