Solving Equations by Extracting Roots

AII.4b

Solving Equations with ExponentsSolve

Isolate the variable

What is the inverse operation to ‘squaring’?

4 𝑥2−36=0

√𝑥2=√9Simplify both sides 𝑥=±3

Why is it ? Remember, we are looking for the value of x, that gives us 9 when it is squared. What is ? What is Anytime you are looking for a value that is squared, you will have a in your answer since squaring both a positive and negative rational number gives you a positive product.

Solving Equations with Exponents

2 81 0x 2 81x 2 81x

9x i

Solve

Isolate the variable

What is the inverse operation to ‘squaring’?

Simplify both sides

Solving Equations with Exponents

22 144 0x 22 144x

2 72x

2 72x

6 2x i

Solve

Isolate the variable

What is the inverse operation to ‘squaring’?

Simplify both sides

Solving Equations with Exponents34 96 0x 34 96x 3 24x

Solve

Isolate the variable

What is the inverse operation to ‘cubing’?

Simplify both sides

3 3 3 24x 32 3x