Solving Equations Involving Cube Roots

Negative Solutions

• When dealing with square roots, we decided that we could not take the square root of a negative number.

• Why can we do this with a cube root?

= -2

Lets Do a Few

=

=

Think Pair Share

• When taking the cube root of a negative number, what must be true about the solution?

Finding the Cube Root of a Fraction

• You can find the cube root of a fraction by taking the cube root of both the numerator and the denominator:

= =

Checking for Understanding

• Simplify

Checking for Understanding

• Simplify

Checking for Understanding

• Simplify

• We could make estimates if the cube roots are not perfect, but typically we simplify the cube root instead by pulling out perfect cubes so that we are keeping exact values.

• That is a topic for another day.

Discussion

• Complete the pattern:

3 x 3 x 3 = 27 = 3 5 x 5 x 5 = 125 = 5 a x a x a = a³ = ___ b x b x b = b³ = ___

c x c x c = c³ = ___

Equations with Roots

= 216

You should be able to look at this and immediately know the value for x that makes the equation true.

We need to be able to prove it with algebra.

Equations with Roots = 216

In all equations, we are looking for the value of 1x, in this case the x has been squared. The inverse of squaring a number is taking the square root. We will do this to both sides of the equation. = 216 =

x = 6

Think Pair Share

• Is there another solution that will satisfy this equation?

= 216 =

NO! -6 cubed will produce a negative solution

• Cube roots have only one possible solution, whereas square roots can have 2.

Checking for Understanding

• Solve for x

x³ = 8

Checking for Understanding

• Solve for x

512 = x³

Checking for Understanding

• Solve for x

x³ = -1000

Estimating Non – Perfect Solutions

• You can use the same process for yesterday to make your estimation

x³ = 40 = x =

3√ 40

Estimating Non – Perfect Solutions

• You can use the same process for yesterday to make your estimation

x³ = 100