Solve Equations with Square Root and Cube Root

Equations with Square and Cube Roots

by Mr. Coffey

​Reminder about equations...

​Example:

​Our goal is always to UNDO the operations around the variable that we are solving for...

​3x + 4 = 16

​

​ -4

​ -4

​3x = 12

x = 4

​ /3

​ /3

Fill in the Blank

Review: What does x equal in this equation?

(Hint: Undo everything on the side of x)

  $$4x-7=9$$  

What about square roots?

<-- Opposites -->

The opposite of taking a square root is... squaring!

​Example:

Fill in the Blank

You try! What does x equal?

$$\sqrt[]{x}=7$$  

What about CUBE roots?

<-- Opposites -->

The opposite of taking a cube root is... you guessed it: cubing!

​Example:

Fill in the Blank

You try! What does x equal?

$$\sqrt[3]{x}=4$$  

Multiple Choice

Let's practice! Solve for a.

(Hint: Undo the square LAST)

$$3\sqrt[]{a}=6$$  

• 2

• 4

• 6

• 9

Multiple Choice

Solve for b.

(Hint: Undo the square LAST)

$$\sqrt[]{a}-9=-3$$  

• 24

• 17

• 27

• 36

Multiple Choice

Solve for y.

$$2\sqrt[3]{y}=10$$  

• 125

• 20

• 5

• 75

Multiple Choice

Solve for x.

(Hint: What are we multiplying $$\sqrt[3]{x}$$  by?)

$$-\sqrt[3]{x}=-7$$  

• -343

• 49

• 343

• -49

Multiple Choice

Solve for h.

(Hint: Begin with adding/subtracting)

$$-2\sqrt[3]{x}-3=-7$$  

• 21

• -5

• 8

• -12