Solving Radical Equations (More Challenging)

Learn how to solve more challenging radical equations in this free math video tutorial by Mario's Math Tutoring.

0:12 Example 1 Solving Square Root (3x-8) + 1 = Square Root (x+5)
0:30 Step 1 Isolate 1 Radical and Square Both Sides
1:23 Isolate Remaining Square Root On One Side of the Equation and Square Both Sides to Eliminate the Square Root
2:42 Factor and Set Factors Equal to Zero
2:55 Check Solutions in Original Equation to Check for Extraneous (False) Roots

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Solving Radical Equations

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[agentmischief]

our teacher never thought us this but this was our homework and like- are you serious right now

[frankgrimes]

Nice video help me out a lot I was stuck on this one problem because I forgot I was supposed to divide by 2

[dzpismu]

I think it would be good to use substitution as:
3x-8=y^2
x+5=z^2
y+1=z
eliminate the x from first two equations, replace z by y+1,
then we can find the two roots of y more easily.

[tetrisyag]

Thank you so much! I was stuck on a problem like this because I kept thinking the first squaring would get rid of both square roots. Thanks again :D

[theroman]

Do You Have Shortcuts for Competitions for solving it under a minute?

[matthewhosier]

one minute in and i already had every question answered lol

[touhami]

At 2sqrt(3x-8) = -2x+12 :
BEFORE SQUARING, involve THE CONDITION:
-2x+12 >=0 ===> x<=6 D of validity

4(3x-8) = (-2x+12)^2 ==> x=4 or x=11 in D
Only 4 is IN D so S= { 4 }.

[AyhamEmad]

I do have a question.What if i get imaginary solutions to a cube root equation, are these solutions extraneous for sure?

[machogwapito]

What if the number 1 in the first radical is in the front? Not after the radical?

[MinhTran-ftrc]

Great video! Helped me out a lot, though it was complicated, but I soon understood it! One quick question, if you had a question like this, but there were binomials on both sides, what would you do?

[jerrypaquette]

11 does work if you consider that the sqrt. of 25 is +- 5 and sqrt. of 16 +- 4 : -5 +1 = -4

[gowin]

Should derivatives at either side of the equation are brought to zero and a variable is left, then equation may be an extraneous as the case.

[gep]

You are the best man! I am preparing to take a quiz and I was stuck on this problem.

[palecolt]

I tried to do this exactly the way you did and it did not work in the slightest. I kept getting fractions when you go to divide whatever number is next to the square root.

[machogwapito]

What if the number 1 in the first radical is in the front? Not after the radical?