Solving radical equations

Lesson: 1a
18:09
Lesson: 1b
6:43
Lesson: 1c
8:52
Lesson: 1d
3:08
Lesson: 2a
10:20
Lesson: 2b
6:04
Lesson: 2c
3:22
Lesson: 2d
8:50

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Solving radical equations

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.

Basic concepts: Converting radicals to entire radicals, Adding and subtracting radicals, Multiplying and dividing radicals, Rationalize the denominator ,

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)

Solving radical equations

Solving radical equations

Lessons

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