Radical Equations Notes

Radical Equations Notes

How to find a 3rd, 4th, 5th, etc. root on a calculator

We'll find the 4th root of 81

• Figure out if your calculator has ^ or y^x as the exponent button

• Select the following buttons if your calculator has ^

• 4 > 2nd > ^ > 81 > =

• Select the following buttons if your calculator has y^x

• 81 > 2nd > y^x > 4 > =

• You should get 3 as your answer

Multiple Choice

How do you think you would get x by itself in

 $\sqrt{x}=3$  ?

• square both sides

• take the square root of both sides

• multiply by the square root

• multiply by 2

Multiple Select

What did I say are the two big steps in these radical equation problems?

• get rid of the fractions

• isolate the radical

• move everything to one side of the equal sign

• get rid of the radical

Multiple Choice

What should you do first to try to solve this equation? $^3\sqrt{2x-5}-6=-3$  

• subtract -5-6

• add 6 to the other side

• subtract 6 to the other side

• divide by -6

Multiple Choice

Now what? 

 $^3\sqrt{2x-5}=3$  

• square both sides

• cube both sides

• divide by 3

• add 5

• take the cube root of both sides

Multiple Choice

What is the result when you cube both sides?

 $^3\sqrt{2x-5}=3$  

•  $8x^3-125=27$  

•  $2x^3-125=27$  

•  $2x-5=3$  

•  $2x-5=27$  

Multiple Choice

Solve for x.

 $2x-5=27$  

• 64

• 11

• 16

• 6

Multiple Choice

When can extraneous solutions arise?

• in any kind of radical equation

• when you raise both sides to an even exponent

• when you raise both sides to an odd exponent

• when you do the problem wrong

Multiple Choice

True or False:

(x+6)² = x²+36

• True

• False

Multiple Choice

What should you do first to solve for x?

 $1+^4\sqrt{x-2}=3$  

• add 1

• square both sides

• raise both sides to the 4th power

• subtract 1

• add 2

Multiple Choice

Now what?

 $^4\sqrt{x-2}=2$  

• raise both sides to the 4th power

• add 2 to the other side

• divide by 2

• divide by 4

• square both sides

Multiple Choice

Solve for x.

 $x-2=2^4$  

• 6

• 10

• 16

• 18

• 8

Multiple Choice

Check your answer x=18 by plugging it into the original equation.

 $1+^4\sqrt{x-2}=3$  

• it's valid

• it's extraneous

Multiple Choice

 $x-3=\sqrt{-2x+41}$  

Solve for x.

• 8

• -4

• 4

• no solution

• -8

Multiple Choice

 $x-3=\sqrt{-2x+41}$  
What is the extraneous solution?

• 8

• 4

• -4

• -8

• none

Multiple Choice

Select the equivalent form of $^3\sqrt{x^8}$  

•  $x^{\frac{8}{3}}$  

•  $x^{\frac{3}{8}}$  

Multiple Choice

Solve.

 $x+^3\sqrt{5x-2}-3=x-4$  

• -5

• 3/5

• -1/5

• 5

• 1/5